We find closed formulas for arbitrarily high mixed moments of characteristic polynomials of the Alternative Circular Unitary Ensemble, as well as closed formulas for the averages of ratios of characteristic polynomials in this ensemble. A comparison is made to analogous results for the Circular Unitary Ensemble. Both moments and ratios are studied via symmetric function theory and a general formula of Borodin-Olshanski-Strahov.

Let ${\mathfrak g}$ be a complex simple Lie algebra and ${\mathfrak n}$ the nilradical of a parabolic subalgebra of ${\mathfrak g}$. We consider some properties of the coadjoint representation of ${\mathfrak n}$ and related algebras of invariants. This includes (i) the problem of existence of generic stabilizers, (ii) a description of the Frobenius semiradical of ${\mathfrak n}$ and the Poisson center of the symmetric algebra , (iii) the structure of as -module, and (iv) the description of square integrable (= quasi-reductive) nilradicals. Our main technical tools are the Kostant cascade in the set of positive roots of ${\mathfrak g}$ and the notion of optimization of ${\mathfrak n}$.

Metabolomics has been utilised in epidemiological studies to investigate biomarkers of nutritional status and metabolism in relation to non-communicable diseases. However, little is known about the effect of prandial status on several biomarker concentrations. Therefore, the aim of this intervention study was to investigate the effect of a standardised breakfast meal followed by food abstinence for 24 h on serum concentrations of amino acids, one-carbon metabolites and B-vitamin biomarkers. Thirty-four healthy subjects (eighteen males and sixteen females) aged 20–30 years were served a breakfast meal (∼500 kcal) after which they consumed only water for 24 h. Blood samples were drawn before and at thirteen standardised timepoints after the meal. Circulating concentrations of most amino acids and metabolites linked to one-carbon metabolism peaked within the first 3 h after the meal. The branched-chain amino acids steadily increased from 6 or 8 hours after the meal, while proline decreased in the same period. Homocysteine and cysteine concentrations immediately decreased after the meal but steadily increased from 3 and 4 hours until 24 h. FMN and riboflavin fluctuated immediately after the meal but increased from 6 h, while folate increased immediately after the meal and remained elevated during the 24 h. Our findings indicate that accurate reporting of time since last meal is crucial when investigating concentrations of certain amino acids and one-carbon metabolites. Our results suggest a need for caution when interpretating studies, which utilise such biomarkers, but do not strictly control for time since the last meal.

This paper proposes a novel approach to assessing the efficiency and distributional consequences of occupational licensing statutes during the Gilded and Progressive eras, based on the practice of judicial review. At the time, state judges ruling on the constitutionality of police powers regulation operated under powerful legal norms that militated against redistribution and class legislation. Evidence presented in the paper strongly suggests that judges were significantly more likely to uphold, on constitutional grounds, occupational licensing legislation for occupations with important information asymmetries, suggesting that constitutional review promoted efficiency in occupational markets. These findings have implications for current policies regarding occupational licensing.

Oldest-old (age 80+) spousal care-givers of people with dementia experience unique challenges and concerns that they attribute to age and/or ageing, including difficulties providing care because of physical, cognitive or sensory decline; having fewer friends who can provide practical support; and having less energy for non-care-giving activities (e.g. leisure activities, self-care). Previous research on how older care-givers manage is not specific to oldest-old care-givers and may underrepresent their unique experiences managing age and ageing-related challenges. A limited understanding can compromise our ability to tailor services to ageing care-givers. The purpose of this research was to illuminate how oldest-old spousal care-givers of people with dementia manage ageing-related care-giving challenges and the barriers and facilitators to strategy use. The selective optimisation with compensation theory and the transactional theory of stress and coping informed our conceptualisation of management strategies. We used a narrative gerontology approach, with two or three semi-structured interviews with 11 care-givers aged 80–89 (25 interviews in total). Narrative data were analysed thematically. We identified four main themes that encompassed the strategies shared by care-givers: adjusting goals to lessen care-giving demands and to mitigate stress, using alternative means to reach goals and to mitigate stress, enhancing capacities to care and mitigate stress through engagement in non-care-giving activities, and choosing positive attitudes and perspectives to lessen emotional distress. We identified a myriad of facilitators and barriers to strategy utilisation in each theme. The study provides unique insight into care-givers' management strategies, especially in relation to relocation of self and spouse and participation in non-care-giving activities, as well as insight into age-related facilitators and barriers. This research can ultimately help inform the tailoring of age-sensitive health and social care services to meet the needs of this group of care-givers as they age.

Several meta-analyses investigating the efficacy of n-3 PUFA in alleviating depression symptoms have reported conflicting findings. In the present study, we aimed to perform an umbrella meta-analysis to provide a definite conclusion. A comprehensive systematic search of PubMed, Scopus, Embase, Web of Science and Cochrane Central Library was performed up to June 2021. Meta-analysis studies evaluating the effects of n-3 PUFA on depression symptoms were included. The quality of the included meta-analyses was assessed using AMSTAR questionnaire. Out of 101 studies, twenty-two studies with twenty-six effect sizes (ES) were eligible for inclusion. Sixteen ES showed significant improving effect of n-3 supplementation on depression symptoms among which eleven ES had small ES. The other studies observed no significant effect. Available evidence suggests that n-3 PUFA (EPA, DHA) supplementation could be considered as an effective add-on therapeutic approach in relieving depression symptoms.

The Episcopal Church has been engaged in efforts to revise its Book of Common Prayer since the mid-1990s, but a completed revision is still nowhere in sight. This essay explains the process for revision in the Episcopal Church, the working of that process leading up to the adoption of the Book of Common Prayer 1979 and the optimism about a further revision in the 1990s. It then seeks to understand the inability of the Episcopal Church to follow through on the hope of revision in the first two decades of the twenty-first century, despite considerable work on liturgical texts and the involvement of a growing number of task forces and special committees. It follows with discussion of the issues related to revision before the 2022 and the upcoming 2024 conventions and concludes with reflections on the obstacles to a completed revision.

For every $n\geq 2$, Bourgain’s constant $b_n$ is the largest number such that the (upper) Hausdorff dimension of harmonic measure is at most $n-b_n$ for every domain in $\mathbb {R}^n$ on which harmonic measure is defined. Jones and Wolff (1988, Acta Mathematica 161, 131–144) proved that $b_2=1$. When $n\geq 3$, Bourgain (1987, Inventiones Mathematicae 87, 477–483) proved that $b_n>0$ and Wolff (1995, Essays on Fourier analysis in honor of Elias M. Stein (Princeton, NJ, 1991), Princeton University Press, Princeton, NJ, 321–384) produced examples showing $b_n<1$. Refining Bourgain’s original outline, we prove that

$$\begin{align*}b_n\geq c\,n^{-2n(n-1)}/\ln(n),\end{align*}$$

$n\geq 3$

$c>0$

$b_3\geq 1\times 10^{-15}$

$b_4\geq 2\times 10^{-26}$

Offshoring and automation are sources of wage polarization. We reassess these two determinants of wage polarization in a single directed technical change setup that encompasses routine and nonroutine production. We empirically establish the conditional positive relationship between automation and relocations on one side and wage polarization on the other. Theoretically, we show that wage polarization increases with automation and offshoring. In particular, wage polarization in favor of domestic (nonroutine) high(low)-skilled workers is positively affected by an increase in domestic (nonroutine) high(low)-skilled labor quantity and/or absolute productivity. Additionally, it is also positively influenced by a rise in foreign (routine) medium-skilled labor quantity and/or absolute productivity while negatively impacted by an increase in domestic (routine) medium-skilled labor quantity and/or absolute productivity. We show that the effect of offshoring on wage polarization diminishes with the degree of substitutability between routine and nonroutine sectors in the economy, with the share of machines in the production of intermediate goods, and with the scale effect. We quantitatively assess the impact through a thorough data-based calibration exercise, where the numerical results confirmed the theoretical findings.

Teleparallel gravity, an empirically equivalent counterpart to general relativity, represents the influence of gravity using torsional forces. It raises questions about theory interpretation and underdetermination. To better understand the torsional forces of teleparallel gravity, we consider a context in which forces are better understood: classical spacetimes. We propose a method of incorporating torsion into the classical spacetime context that yields a classical theory of gravity with a closed temporal metric and spacetime torsion. We then prove a result analogous to the Trautman degeometrization theorem: that every model of Newton–Cartan theory gives rise, non-uniquely, to a model of this theory.

X-ray powder diffraction data, unit-cell parameters, and space group for the Lumateperone tosylate, C24H29FN3O⋅C7H7O3S, are reported [a = 15.5848(10) Å, b = 6.0700(4) Å, c = 31.3201(14) Å, β = 96.544(5)°, V = 2943.58 Å3, Z = 4, and space group C2]. In each case, all measured lines were indexed and were consistent with the corresponding space group. The single-crystal data of Lumateperone tosylate is also reported, respectively [a = 15.626(3) Å, b = 6.0806(10) Å, c = 31.415(5) Å, β = 96.609(7)°, V = 2965.1(8) Å3, Z = 4, and space group C2]. The experimental powder diffraction pattern has been well matched with the simulated pattern derived from the single-crystal data with preferred orientation in the [002] direction (orientation coefficient = 0.75).

The palatal nasal is one of French’s most variable consonants with attested variants including [ɲ] alongside [nj] and, less frequently, [n] and [ŋ]. Variation is conditioned by both linguistic (position in the word, lexical item, flanking vowels) and speaker variables (in particular, variety). Except for insights provided by the studies reviewed in Recasens (2013), little is known of the articulatory properties of French /ɲ/ including the degree of inter-varietal and -speaker variation or the proportion of coronal and velar depalatalized realizations. We present here an electropalatographic (EPG) study of two European (EF) and two Quebec French (QF) speakers’ /ɲ/ production in both word-medial and -final positions in isolated and contextualized words. Quantitative indices and qualitative investigation of the linguopalatal contact profiles reveal that the EF speakers produced a relatively anterior /ɲ/, differing minimally from /n/ followed by /j/. Whereas one of their QF peers produced uniquely backed velar realizations of /ɲ/, the other speaker had fronted alveolopalatal variants word-medially versus backed velar realizations word-finally, with the latter differing minimally from the /ŋ/ of jogging. These findings are consistent with pathways to depalatalization observed in other Romance varieties and call into question the phonemic status of the palatal nasal in French.