We show that if an open set in $\mathbb{R}^d$ can be fibered by unit n-spheres, then $d \geq 2n+1$, and if $d = 2n+1$, then the spheres must be pairwise linked, and $n \in \left\{0, 1, 3, 7 \right\}$. For these values of n, we construct unit n-sphere fibrations in $\mathbb{R}^{2n+1}$.

With the advancement of medical technology, there are increasing opportunities for new-borns, infants, and pregnant women to be exposed to general anaesthesia. Propofol is commonly used for the induction of anaesthesia, maintenance of general intravenous anaesthesia and sedation of intensive-care children. Many previous studies have found that propofol has organ-protective effects, but growing evidence suggests that propofol interferes with brain development, affecting learning and cognitive function. The purpose of this review is to summarize the latest progress in understanding the neurotoxicity of propofol. Evidence from case studies and clinical studies suggests that propofol has neurotoxicity on the developing brain. We classify the findings on propofol-induced neurotoxicity based on its damage mechanism. We end by summarizing the current protective strategies against propofol neurotoxicity. Fully understanding the neurotoxic mechanisms of propofol can help us use it at a reasonable dosage, reduce its side effects, and increase patient safety.

Let $U$ be a smooth affine curve over a number field $K$ with a compactification $X$ and let ${\mathbb {L}}$ be a rank $2$, geometrically irreducible lisse $\overline {{\mathbb {Q}}}_\ell$-sheaf on $U$ with cyclotomic determinant that extends to an integral model, has Frobenius traces all in some fixed number field $E\subset \overline {\mathbb {Q}}_{\ell }$, and has bad, infinite reduction at some closed point $x$ of $X\setminus U$. We show that ${\mathbb {L}}$ occurs as a summand of the cohomology of a family of abelian varieties over $U$. The argument follows the structure of the proof of a recent theorem of Snowden and Tsimerman, who show that when $E=\mathbb {Q}$, then ${\mathbb {L}}$ is isomorphic to the cohomology of an elliptic curve $E_U\rightarrow U$.

Dispersive and Strichartz estimates are obtained for solutions to the wave equation with a Laguerre potential in spatial dimension three. To obtain the desired dispersive estimate, based on the spectral properties of the Schrödinger operator involved, we subsequently prove the dispersive estimate for the corresponding Schrödinger semigroup, obtain a Gaussian-type upper bound, establish Bernstein-type inequalities, and finally pass to the Müller–Seeger’s subordination formula. The desired Strichartz estimates follow by the established dispersive estimate and the standard argument of Keel–Tao.

We discuss a strategy for classifying anomalous actions through model action absorption. We use this to upgrade existing classification results for Rokhlin actions of finite groups on C$^*$-algebras, with further assuming a UHF-absorption condition, to a classification of anomalous actions on these C$^*$-algebras.

In this paper, we mainly prove the following conjectures of Sun [16]: Let p > 3 be a prime. Then

\begin{align*}&A_{2p}\equiv A_2-\frac{1648}3p^3B_{p-3}\ ({\rm{mod}}\ p^4),\\&A_{2p-1}\equiv A_1+\frac{16p^3}3B_{p-3}\ ({\rm{mod}}\ p^4),\\&A_{3p}\equiv A_3-36738p^3B_{p-3}\ ({\rm{mod}}\ p^4),\end{align*}

where $A_n=\sum_{k=0}^n\binom{n}k^2\binom{n+k}{k}^2$ is the nth Apéry number, and Bn is the nth Bernoulli number.

Given any polynomial in two variables of degree at most three with rational integer coefficients, we obtain a new search bound to decide effectively if it has a zero with rational integer coefficients. On the way we encounter a natural problem of estimating singular points. We solve it using elementary invariant theory but an optimal solution would seem to be far from easy even using the full power of the standard Height Machine.

Chickpea is a cool season, photothermal-sensitive crop, that is adversely affected by high temperatures (>35°C) and whose flowering is promoted by long-day conditions (>12 h). This prevents horizontal crop spread under a variety of agro-climatic conditions and the development of insensitive genotypes that perform well in all seasons. Therefore, a study was conducted to identify genotypes that are mature early, insensitive to photoperiod, high temperature and tolerant to drought stress. A set of 74 genotypes was evaluated under rainfed conditions in Kharif 2021 (off-season) to select eight promising early-maturing genotypes with high-yielding capacity. Then further investigations were conducted in five different seasons Late Kharif 2021, rabi 2021, summer 2022, early Kharif 2022 and Kharif 2022 to identify the genotypes with photothermo-insensitivity among the selected eight genotypes. With the exception of rabi 2021, each of these seasons were distinct from the chickpea's typical growing season. Among these eight, the stable genotypes which are performed better in all the seasons, especially in summer were considered, such as IPC 06-11, MNK-1, JG-14 and ICE 15654-A as a photothermo-insensitive, were able to flower and set pods with higher seed yield and, resulting in early maturity in a temperature range of 41.4/9.3°C with photoperiods of 13.1/10.9 h to reach in all seasons throughout the year. The heritability was more than 60%. Hence, these genotypes can be used as donor aids in the development of early maturing, drought stress tolerant and photothermo-insensitive chickpea.

Medical trainees (applicants, students, and house officers) often engage in global health initiatives to enhance their own education through research and patient care. These endeavors may concomitantly prove of value to host nations in filling unmet clinical needs. At present, healthcare institutions generally focus on the safety of the trainee and the welfare of potential patients and research subjects when sanctioning such programs. The American medical community has historically afforded less consideration to the ethics of engagement by trainees from the United States in nations known for serious human rights transgressions. This essay examines the ethics of such endeavors and argues for increased consideration of these broader considerations when trainees engage in global health work abroad.

Social movements often appeal to the politics of sight, meaning that if people knew about a given injustice, political transformation would follow. Jasmine English and Bernardo Zacka articulate two central premises of the politics of sight: “(1) exposing morally repugnant practices will make us see them, (2) seeing such practices will stop us from acquiescing to them.” Considering the case of slaughterhouse workers, Timothy Pachirat and English and Zacka challenge the previous premises. This article complements their contributions by theorizing what I call Western conceptuality/language and the role this plays in forming our subjectivities not to recognize violence on the one hand, and to be sovereign masters over animals on the other. I conclude by discussing the political implications of these arguments for the politics of sight, including the role of concealment and exposure, and the conditions needed for humans to see animals in their full ethical weight.

In this article, we investigate the spectra of the stability and Hodge–Laplacian operators on a compact manifold immersed as a hypersurface in a smooth metric measure space, possibly with singularities. Using ideas developed by A. Ros and A. Savo, along with an ingenious computation, we have obtained a comparison between the spectra of these operators. As a byproduct of this technique, we have deduced an estimate of the Morse index of such hypersurfaces.

Epidemiologic research has increasingly acknowledged the importance of developmental origins of health and disease (DOHaD) and suggests that prior exposures can be transferred across generations. Multigenerational cohorts are crucial to verify the intergenerational inheritance among human subjects. We carried out this scoping review aims to summarize multigenerational cohort studies’ characteristics, issues, and implications and hence provide evidence to the DOHaD and intergenerational inheritance. We adopted a comprehensive search strategy to identify multigenerational cohorts, searching PubMed, EMBASE, and Web of Science databases from the inception of each dataset to June 20th, 2022, to retrieve relevant articles. After screening, 28 unique multigenerational cohort studies were identified. We classified all studies into four types: population-based cohort extended three-generation cohort, birth cohort extended three-generation cohort, three-generation cohort, and integrated birth and three-generation cohort. Most cohorts (n = 15, 53%) were categorized as birth cohort extended three-generation studies. The sample size of included cohorts varied from 41 to 167,729. The study duration ranged from two years to 31 years. Most cohorts had common exposures, including socioeconomic factors, lifestyle, and grandparents’ and parents’ health and risk behaviors over the life course. These studies usually investigated intergenerational inheritance of diseases as the outcomes, most frequently, obesity, child health, and cardiovascular diseases. We also found that most multigenerational studies aim to disentangle genetic, lifestyle, and environmental contributions to the DOHaD across generations. We call for more research on large multigenerational well-characterized cohorts, up to four or even more generations, and more studies from low- and middle-income countries.

We generalize to a broader class of decoupled measures a result of Ziv and Merhav on universal estimation of the specific cross (or relative) entropy, originally for a pair of multilevel Markov measures. Our generalization focuses on abstract decoupling conditions and covers pairs of suitably regular g-measures and pairs of equilibrium measures arising from the “small space of interactions” in mathematical statistical mechanics.

Research internationally has revealed a range of medical and health-related issues that shape care at the end of life for people living in residential aged care facilities (RACFs), their families and the staff who care for them. Yet, less is known about the lived experiences of residents, and the broader socio-cultural, emotional and relational factors that shape experiences of dying within such settings. In this article, we present findings from a scoping review designed to establish what is known about the lived experience of residents nearing the end of life. In doing so, we identify research gaps and move towards an agenda for future research. Five electronic databases were used to identify empirical research articles investigating end-of-life experiences from the perspective of older people living in RACFs, from which we selected 22 papers for thematic analysis. Our analysis highlighted three key themes: connections and closeness; place and the end of life; and temporality, care and the anticipation of dying. A majority of the articles (15) highlighted the importance of social connectedness with staff, co-residents and family in enabling people to die with dignity and a sense of belonging in residential settings. The physical layout and living arrangements in RACFs were found to affect the ways in which residents relate within the space, especially during and after the death of a resident. Anticipatory fears of dying were oriented towards the context of illness and care, and its management within the RACF, rather than death itself. Our analysis highlights considerable evidence that ‘good deaths’ are embedded in experiences of socio-emotional wellbeing, connectedness and relationality. However, much of the extant research analysed is exploratory, pointing to the need for further social scientific study of the social and cultural embeddedness of end-of-life experiences with residential aged care.