In this paper, we give necessary and sufficient conditions for the rigidity of the perimeter inequality under Schwarz symmetrization. The term rigidity refers to the situation in which the equality cases are only obtained by translations of the symmetric set. In particular, we prove that the sufficient conditions for rigidity provided in M. Barchiesi, F. Cagnetti and N. Fusco [Stability of the Steiner symmetrization of convex sets. J. Eur. Math. Soc. 15 (2013), 1245-1278.] are also necessary.

This article examines passive-type constructions in Mauritian Creole, arguing that they are topic, not passive constructions. I claim that their initial argument (the displaced object) occupies the specifier position of a Topic Phrase, not the structural subject position. This proposal is motivated by the fact that nothing at the surface identifies the displaced object as a grammatical subject, except its position relative to an auxiliary or verb. The topic analysis is supported by both semantic restrictions relating to specificity and animacy and syntactic restrictions relating to distribution (word order) and coordination. It is also supported by the fact that these same restrictions do not apply in unaccusatives, a structurally similar type of construction. The important contribution of this article is that passive-type constructions in Mauritian Creole are ‘apparent’ rather ‘real’ passives, with the wider implication being that creoles, like many languages, do not use canonical passives to express passive meaning.

The English, and later British, settlement of Bencoolen was first established in 1685 and remained in British hands, barring French wartime occupation, until 1825, when it was handed over to the Dutch in a territorial exchange. Bencoolen was even elevated to the status of a Presidency in the second half of the eighteenth century. Why did the English East India Company and British officials maintain a presence in Bencoolen for so long? This article makes the case that multiple, overlapping visions of commercial and agrarian transformation, including projects focused on pepper and sugar cultivation, sustained British efforts to govern and maintain Bencoolen as part of a larger, trans-oceanic network of territories. Such visions of Bencoolen's economic and imperial potential evolved in sync with equally persistent concerns about Bencoolen's failure to become a thriving settlement. Yet even amid constant anxieties about producing enough pepper, maintaining a sizeable population, and generating sufficient revenue, numerous British imperial agents located in London and Calcutta as well as Sumatra argued over whether the settlement was likely to remain a permanent failure and how the problems that dogged it might be resolved. Thus, even in moments when Bencoolen appeared to be a failed outpost on the periphery of a growing British Empire, its success or lack thereof commanded the attention of British ministers and East India Company servants. In calling for Bencoolen's elevation, subordination, or even abolition as a settlement, Britons contributed to a wide-ranging discussion of what constituted a valuable colony and, indeed, empire.

Retinopathy of prematurity (ROP) is a leading cause of blindness in premature infants. The condition is associated with DHA deficiency. This study aimed to investigate the effect of DHA supplementation on the occurrence of ROP in infants receiving oral oil drops. It is part of the Joinville DHA study, a non-parallel-group cohort study conducted from March 2020 to January 2023 at a public maternity hospital in Brazil. Infants born before 33 weeks of gestational age or with a birth weight ≤ 1500 g were recruited. Among 155 infants, 81 did not receive and 74 received DHA supplementation until complete vascularisation of the peripheral retina. There was a higher incidence of infants with ROP in the unsupplemented group (58·6 %) compared with the DHA group (41·4 %), but this difference was NS (P = 0·22). Unadjusted logistic regression analysis showed that patent ductus arteriosus and neonatal corticosteroids were significantly (P < 0·05) associated with ROP in both groups. In the DHA group, surfactant use was also associated with ROP (P = 0·003). After adjusting for important covariates, patent ductus arteriosus and neonatal corticosteroids continued to be significant for infants in the unsupplemented group (OR = 3·99; P = 0·022 and OR = 5·64; P = 0·019, respectively). In the DHA group, only surfactant use continued to be associated with ROP (OR = 4·84; P = 0·015). In summary, DHA supplementation was not associated with ROP. Further studies are necessary to better understand the relationship between DHA supplementation, ROP and associated comorbidities.

We consider the existence problem of meromorphic solutions of the Fermat-type difference equation

$$ \begin{align*} f(z)^p+f(z+c)^q=h(z), \end{align*} $$

where $p,q$ are positive integers, and h has few zeros and poles in the sense that $N(r,h) + N(r,1/h) = S(r,h)$. As a particular case, we consider $h=e^g$, where g is an entire function. Additionally, we briefly discuss the case where h is small with respect to f in the standard sense $T(r,h)=S(r,f)$.

Polycystic ovary syndrome is associated with increased risks for certain metabolic disorders such as insulin resistance, non-alcoholic fatty liver disease and suppressed ovarian follicular development. This study aimed to examine whether soya isoflavones (ISF) mitigate these polycystic ovary syndrome-associated metabolic disorders in a rat model. Weanling Sprague-Dawley female rats were randomly divided into six groups and were treated with either 0 or 83 µg/d dihydrotestosterone (DHT) to induce polycystic ovary syndrome and fed diets containing 0, 0·5, or 1 g ISF/kg diet for 8 weeks. DHT treatment increased food intake, body weight gain (P < 0·001), percentage of primordial follicles (60 % v. 50·9 %, P < 0·05) and accumulation of lipid droplets in the livers. It also elevated serum total cholesterol, free cholesterol, TAG, NEFA and leptin and hepatic total cholesterol and NEFA. Additionally, DHT treatment reduced the percentage of primary follicles (13·8 % v. 30·2 %, P < 0·05), ovary weight and length (P < 0·001), as well as insulin sensitivity (P < 0·01) compared with the Control. ISF intake at 1 g/kg reduced body weight gain, serum total cholesterol, free cholesterol, NEFA, leptin and hepatic TAG and DHT-induced insulin resistance (P < 0·01). ISF intake at both levels decreased DHT-induced lipid droplet accumulation in the livers and changes in the percentages of primordial and primary follicles. Dietary soya ISF alleviated DHT-induced body weight gain, insulin resistance and hepatic lipid droplet accumulation, as well as suppressed ovarian follicular development. This suggests that the consumption of soya foods or ISF supplements may be beneficial for individuals with polycystic ovary syndrome, mitigating the associated metabolic disorders such as diabetes and non-alcoholic fatty liver disease.

As ancient China and Rome transformed into empires, both states showed an increasing interest in regulating family ethics and individuals’ sexuality. Using excavated documents and transmitted texts, this article compares legal statutes and practices against illicit consensual sex in early imperial China (221 BCE–220 CE) with those in the Roman empire. On the one hand, both legal systems aimed at consolidating social hierarchies based on gender, status, and generation. On the other, the Roman and Chinese statutes had different emphases due to their respective political, social, and cultural contexts, and the actual penalties for adultery and incest differed significantly from those prescribed in the statutes. In both empires, control over individuals’ sexuality facilitated state power’s penetration into the family during empire-building, giving rise to laws in areas that had been largely left to customs and individual will.

This article examines animals and animality in Hannah Arendt's political thought by focusing on the phenomenological approach she develops in The Life of the Mind. Building on the works of Adolf Portmann and Maurice Merleau-Ponty, Arendt invites us to understand the world in terms of the plurality of all living things who appear to each other in anticipation of being perceived in their distinctness. While Arendt's phenomenology is generative for rethinking politics beyond human exclusivity, it also sits uneasily with her anthropocentric claims that risk reducing animals to reactive organisms driven by biological necessity. Mobilizing Arendt's phenomenology against her anthropocentrism, the article outlines a worldly politics in which all living things engage in multitudinous forms of intra- and interspecies encounter, reciprocity, and responsiveness. To illustrate this worldly politics, the article revisits Arendt's famous call for “a right to have rights” and engages with the debates on animal rights.

Marathon runners, subjected to intense training regimens and prolonged, exhaustive exercises, often experience a compromised immune response. Probiotic supplementation has emerged as a potential remedy to mitigate the impact of prolonged exercise on athletes. Consequently, this study sought to assess the influence of probiotic supplementation on monocyte functionality both before and after the official marathon race. Twenty-seven runners were randomly and double-blindly assigned to two groups: placebo (n 13) and probiotic (PRO) (n 14). Over 30 d, both groups received supplements – placebo sachets containing maltodextrin (5 g/d) and PRO sachets containing 1 × 1010 colony-forming unit Lactobacillus acidophilus and 1 × 1010 colony-forming unit Bifidobacterium bifidum subsp. lactis. Blood samples were collected, and immunological assays, including phagocytosis, hydrogen peroxide production, cytokine levels and monocyte immunophenotyping, were conducted at four different intervals: baseline (start of supplementation/30 d pre-marathon), 24 h-before (1 d pre-marathon), 1 h-after (1 h post-marathon) and 5 d-after (5 d post-marathon). Monocyte populations remained consistent throughout the study. A notable increase in phagocytosis was observed in the PRO group after 30 d of supplementation. Upon lipopolysaccharide stimulation, both PRO and placebo groups exhibited decreased IL-8 production. However, after the marathon race, IL-15 stimulation demonstrated increased levels of 5 d-after, while IL-1-β, IL-8, IL-10, IL-15 and TNF-α varied across different intervals, specifically within the PRO group. Probiotic supplementation notably enhanced the phagocytic capacity of monocytes. However, these effects were not sustained post-marathon.

Spermatogenesis is a highly complex process through which mature sperms are produced, and it requires three important stages; mitosis, meiosis and sperm formation. The expression of genes regulated by transcription factors at specific stages exerts important regulatory effects on the development process of germ cells. Male mice with overexpressed programmed death ligand 1 (PD-L1) (B7 homolog1) in the testis have infertility and abnormal sperm development, thereby exhibiting severe malformation and sloughing throughout spermatid maturation and collapsed and disorganized seminiferous epithelium structure. Furthermore, PD-L1 overexpression causes overexpression of cysteine-rich secretory protein 1 (CRISP1) in the epididymis and adversely affects or precludes sperm energization, sperm-pellucida binding and sperm-oocyte fusion. These findings suggest that CRISP1 and PD-L1 can interact with each other to induce male infertility and germ-cell dissociation.

This study aimed to investigate whether psychological distress, whole-grain consumption and tryptophan metabolism are associated with participants undergoing weight management intervention. Seventy-nine women and men (mean age 49·7 (sd 9·0) years; BMI 34·2(sd 2·5) kg/m2) participated in a 7-week weight-loss (WL) period and in a 24-week weight maintenance (WM) intervention period. Whole-grain consumption was measured using 4 d food diaries. Psychological distress was assessed with the General Health Questionnaire-12 (GHQ), and participants were divided into three GHQ groups based on the GHQ scores before WL. Tryptophan metabolites were determined from the participants’ fasting plasma using liquid chromatography-MS. GHQ scores were not associated with the whole-grain consumption. A positive association was observed between the whole-grain consumption and indole propionic acid (IPA) during the WM (P = 0·033). Serotonin levels were higher after the WL in the lowest GHQ tertile (P = 0·033), while the level at the end of the WM was higher compared with other timepoints in the highest GHQ tertile (P = 0·015 and P = 0·001). This difference between groups was not statistically significant. Furthermore, levels of several tryptophan metabolites changed within the groups during the study. Tryptophan metabolism changed during the study in the whole study group, independently from the level of psychological distress. The association between whole-grain consumption and IPA is possibly explained by the effects of dietary fibre on gut microbiota. This broadens the understanding of the pathways behind the health benefits associated with the intake of whole grains.

Prosecutors in adversarial systems are simultaneously expected to be impartial ministers of justice and partisan advocates. Leaving this tension unaddressed can result in poor-quality prosecutorial decision-making. This article develops a novel “dynamic” framework for prosecutors to navigate between and prioritize these competing considerations, which can be used to understand, evaluate, and improve prosecutorial performance. Under this framework, the prioritization should depend on which function the prosecutor is exercising at any given time. The article then deploys primary data collected in Delhi, through court observation and interviews with judges, lawyers, victims, and victim-support persons, to exemplify and justify the framework.

Crystal structures, microtopography, morphologies, elemental compositions, and ionic conductivity have been investigated for Li5-xLa3(Nb,Ta)O12-y using X-ray diffraction (XRD), field-emission analytical scanning and transmission electron microscopies (S/TEM), and electrochemical impedance spectroscopy. Using Rietveld refinements with powder XRD patterns, we determined that the number of Li atoms in the formula is less than 5 and that Li5-xLa3(NbTa)O12-y crystallizes in the cubic garnet structure with a space group Ia-3d. Sintering at varying temperatures (750–1000 °C) for 5 h in an ambient atmosphere produced distinct outcomes. Rietveld refinements disclosed that the sample sintered at 1000 °C (Li3.43(2)La3Nb1.07(2)Ta0.93(2)O12-y, a = 12.8361(7) Å, V = 2114.96(3) Å3) exhibited the highest ionic conductivity, while the 850 °C sample had the lowest conductivity, characterized by lower Li concentration and impurity phases (Li(Nb,Ta)3O88, Li2CO3). Analyses, including XRD and electron microscopy, confirmed the 1000 °C sample as a relatively phase pure with enhanced Li content (Li/La = 1.2), larger grains (15 μm), and uniform crystallinity. The 1000 °C sample introduced additional partially filled Li3 (96h) sites, promoting Li migration, and enhancing ionic conductivity. The resulting XRD pattern at 1000 °C has been submitted to the Powder Diffraction File as a reference.

Orphanhood in Tolstoy has largely escaped critical examination, in part because though the writer himself was an orphan, his texts say little about the topic explicitly. But in fact thinking about orphans' trauma is everywhere in the pre-crisis fiction. Tolstoy draws orphans and non-orphans as fundamentally morally different. All his major protagonists are orphans and want to marry non-orphans. Further, many of his novelistic tics, and many critical insights into Tolstoy generally, actually apply only to characters who are motherless. War and Peace and Anna Karenina can be read as the author's running debate with himself: is an escape available for the traumatized from their pain later in life? If so, it would mean life is good and God is kind. Both books answer yes and demand orphans renounce their permanent sense of grievance against life for their losses. But in their final scenes Tolstoy confesses his optimism was false; life is not fair, and psyches damaged by orphanhood can never fully recover.

Writers and readers cocreate books. Over time, certain readings, even if they are misreadings, come to summarize the book so thoroughly that the book gets transformed into a chapter, a paragraph, a sentence. While chapter 7 of Unmarked, “The Ontology of Performance,” is the most frequently cited, the Afterword’s meditation on misunderstanding may be the most hopeful for future scholarship.