An integer partition of a positive integer n is called t-core if none of its hook lengths is divisible by t. Gireesh et al. [‘A new analogue of t-core partitions’, Acta Arith. 199 (2021), 33–53] introduced an analogue $\overline {a}_t(n)$ of the t-core partition function. They obtained multiplicative formulae and arithmetic identities for $\overline {a}_t(n)$ where $t \in \{3,4,5,8\}$ and studied the arithmetic density of $\overline {a}_t(n)$ modulo $p_i^{\,j}$ where $t=p_1^{a_1}\cdots p_m^{a_m}$ and $p_i\geq 5$ are primes. Bandyopadhyay and Baruah [‘Arithmetic identities for some analogs of the 5-core partition function’, J. Integer Seq. 27 (2024), Article no. 24.4.5] proved new arithmetic identities satisfied by $\overline {a}_5(n)$. We study the arithmetic densities of $\overline {a}_t(n)$ modulo arbitrary powers of 2 and 3 for $t=3^\alpha m$ where $\gcd (m,6)$=1. Also, employing a result of Ono and Taguchi [‘2-adic properties of certain modular forms and their applications to arithmetic functions’, Int. J. Number Theory 1 (2005), 75–101] on the nilpotency of Hecke operators, we prove an infinite family of congruences for $\overline {a}_3(n)$ modulo arbitrary powers of 2.

Axial fans are vital accessories in aircraft ventilation systems, but, they may experience erosion from particulate flows, causing a decline in effectiveness over time. This study investigated the trajectories of two types of sand particles and erosion in an axial fan stage, considering the relative position of the blades facing the inlet guide vanes.

The movement of particles was simulated using an in-house code that implements a Lagrangian approach along with a stochastic particle-eddy interaction model. The flow field was solved separately and the flow data was transferred to the particle trajectory code. The finite element method allowed for the tracking of particles through the computational cells and accurate determination of their impact positions. A semi-empirical erosion correlation was used to evaluate the local erosion rates, mass removal, and geometry deterioration.

As a result, the rotor exhibits a high frequency of impacts and significant erosion on the leading edge of the blade, extending to the upper corner of the pressure side and blade tip, as well as the front of the suction side. In the inlet guide vane, the erosion is spread out along the entire pressure side but at lower erosion rates compared to the rotor blade. The erosion patterns obtained at different pitch-wise positions were cumulated to get better representation of erosion patterns. After being exposed to MIL-E5007E sand (0–1000 $\unicode{x03BC}$m) at the highest concentration for 10 hours, the blade experienced a reduction of a 0.29% in mass, a 0.45% decrease in tip chord, and a 0.23% increase in tip clearance. On the other hand, AC-coarse sand (0–200 μm) resulted in a 0.23% decrease in blade mass, a 0.4% reduction in tip chord, and a 0.16% increase in tip clearance.

The data that is available can be used to monitor the lifespan of axial fans of similar design and select appropriate coatings to protect against erosion.

It is proved that for families of stochastic operators on a countable tensor product, depending smoothly on parameters, any spectral projection persists smoothly, where smoothness is defined using norms based on ideas of Dobrushin. A rigorous perturbation theory for families of stochastic operators with spectral gap is thereby created. It is illustrated by deriving an effective slow two-state dynamics for a three-state probabilistic cellular automaton.

In 1955–6, three thousand German-speaking men were ‘repatriated’ from Czechoslovak forced labour camps, where they mined uranium, to West Germany, where they demanded benefits for health damage from radiation exposure. These men connected their group's experiences to the fears and developments of early Cold War West Germany, personifying the health risks of the Atomic Age and citizens’ demands that their states offer protection from such risks. These men contributed to public awareness of radiation health risk and to ambivalence about safe ‘peaceful nuclear technology’ in the late 1950s and 1960s, earlier than is usually assumed. They further inspired concrete policy changes, especially in occupational health protection, illustrating that post-war responses to nuclear technology emerged from the intersection of longer historical experience, specialised local knowledge and grassroots activism, as well as from post-war scientific and political developments. It further shows long-lasting expellee influence in unexpected areas of West German policy.

Ever more doubts are being raised over the ‘transformative potential’ of the Women, Peace and Security (WPS) agenda and whether it brings us closer to realising feminist peace. Underpinning a current of WPS activism and scholarship is a radical conceptualisation of feminist peace rooted in anti-militarism, anti-capitalism, and anti-imperialism. This strand shares many commonalities with abolition feminism, yet the two literatures and movements are rarely put in conversation. While both begin from similar political commitments and analyses of the international system, they propose radically different solutions for bringing about feminist liberation. Building on this observation, we ask: (1) how would abolition feminism explain why the WPS agenda has often failed to make progress towards a radical vision of feminist peace?; and, as a corollary, (2) what does abolition feminism demand of the WPS agenda? First, using the framework of ‘reformist’ and ‘non-reformist reforms’, we argue that many WPS policies are better understood as reformist rather than transformative. Second, we argue that abolitionist thinking suggests deeper critiques of WPS than those often put forward by its anti-militarist critics, based on a broader conceptualisation of militarism. Ultimately, abolition feminism demands non-reformist, anti-carceral solutions that raise challenging questions about pathways towards feminist peace.

The intra-ovarian presence of ootids, i.e. female gametes that have completed meiosis, is considered exceptional in the animal kingdom. The present study explores the first such case to be reported in a sea cucumber (Echinodermata: Holothuroidea). In the overwhelming majority of animals, including holothuroids, oocytes (i.e. immature female gametes) that are developing in the ovary undergo a primary arrest at the prophase stage of meiosis, which may last from days to decades. In free-spawning taxa, this arrest is normally lifted only during or shortly before transit in the gonoduct, when gamete release (spawning) is imminent. However, oocytes of the holothuroid Chiridota laevis were discovered to have resumed the second meiotic division including the completion of germinal vesicle breakdown and polar-body expulsion inside the ovary, effectively reaching the ootid stage concomitantly with ovulation (i.e. escape from follicle cells) prior to spawning. The potential drivers and significance of this exceptionally rare case of full intra-ovarian oogenic maturation are discussed.

Regolith-hosted rare earth element (REE) deposits hosted by the granitic regolith in South China provide >90% of the world’s heavy REEs. Kaolinite is one of the major carriers of REE ions in regolith. The formation and transformation of kaolinite can be affected by chemical weathering and hydrodynamic conditions, but the contribution of each factor has not been evaluated. This study systematically investigated the variation in abundance of phyllosilicate minerals and structural order of kaolinite in the Renju regolith-hosted REE deposit. The total abundance of 1:1 phyllosilicate minerals increased upwards along the profile from Section I to Section III. However, semi-quantitative analyses indicated that Section III-1 (depth at 10–16 m) featured an evident decrease in both abundance and structural order of kaolinite upward along the profile. The morphological feature and abundance of kaolinite revealed intensive kaolinite-to-halloysite transformation and kaolinite dissolution in Section III-1. This suggests that the alternating wetting and drying zone in Section III-1 provided a favorable kinetic environment for the entry of water molecules into the kaolinite interlayer and the kaolinite-to-halloysite transformation, resulting in both lower structural order and abundance of kaolinite in Section III-1. Moreover, REE ions started to be enriched from the alternating wetting and drying zone and formed high-grade ores at the lower part of the water table, due to a significant increase in pore water and decrease in the seepage velocity. Therefore, the abundance and structural order of secondary kaolinite can serve as important indicators of hydrodynamic changes in regolith, as well as the mineralization of regolith-hosted REEs.

The main objective of the present paper is to present a version of the Tannaka–Krein type reconstruction theorems: if $F:{\mathcal B}\to {\mathcal C}$ is an exact faithful monoidal functor of tensor categories, one would like to realize ${\mathcal B}$ as category of representations of a braided Hopf algebra $H(F)$ in ${\mathcal C}$. We prove that this is the case iff ${\mathcal B}$ has the additional structure of a monoidal ${\mathcal C}$-module category compatible with F, which equivalently means that F admits a monoidal section. For Hopf algebras, this reduces to a version of the Radford projection theorem. The Hopf algebra is constructed through the relative coend for module categories. We expect this basic result to have a wide range of applications, in particular in the absence of fiber functors, and we give some applications. One particular motivation was the logarithmic Kazhdan–Lusztig conjecture.

While the importance of innovation alliance for high-technological firms is well-documented, existing literature provides little guidance on the role of performance feedback in an alliance governance structure choice. Drawing on performance feedback theory, this study sheds light on the association between performance deviating (either above or below) from firms’ social aspirations and the governance structure choice of innovation alliances. Using an unbalanced panel of Chinese biopharmaceutical firms spanning from 2007 to 2020, we find that firms experiencing negative performance feedback prefer a non-equity innovation alliance structure, whereas those with positive performance feedback are more likely to adopt an equity one. The strength of these relationships is contingent on top management team average tenure and educational-level diversity. Our findings both provide theoretical and practical insights into guiding how firms under different states of performance feedback select alliance governance structures.

An enduring puzzle for theorists of autonomy in the broadly Kantian tradition is how to theorize failures of practical reason. If norms of practical rationality are supposed to be constitutive of agency itself, how can failures to live up them nonetheless be understood as expressions of that agency? Hegelian diagnoses of these difficulties typically emphasize the dichotomies that structure Kantian theories of autonomy, between activity and passivity, reason and nature, norm and desire. They seek to flesh out an alternative that preserves a recognisably post-Kantian notion of autonomy whilst understanding freedom as something that essentially comes in degrees, insisting that self-determination always involves elements of other-determination, and stressing how free subjectivity is inseparable from socio-historically and institutionally bounded character-formation. This article contributes to articulating a Hegelian corrective to Kantian theories of autonomy by beginning to explain the role of habit in Hegel's conception of agency. Building on recent work on Hegel's metaphysics of expression, it shows how he allows us to see conative responses to the world as integral to character development and thus as expressive of free agency, rather than as interruptions to the proper functioning of practical reason. On Hegel's account, the expressive behaviour of mature, reflective agents is grounded in a pre-intentional, affective dimension of subjectivity and presupposes processes of habituation, which he locates at the level of the human ‘soul’. Habit, far from being ‘lifeless, contingent and particular’, is the means by which agents come to make objective contents their own. Understanding the role of habit in Hegel's system is integral to allowing an alternative conceptualization of autonomy to come into view, one on which rational agents express themselves through their affective and emotional responses, rather than merely being a contingent site of those responses.

Oat being a rabi/winter crop in Kashmir, experiences extremely low temperatures which has detrimental effects on its growth and development. Therefore, this study was designed to evaluate a set of 130 oat genotypes in multi-location trials across temperate conditions of Kashmir valley from 2018 to 2022. From the preliminary data of 56 genotypes, including five checks, were selected and evaluated for nutritional and yield attributing traits under cold stress conditions at two locations. The results demonstrated significant genetic variation and high heritability for majority of traits, except for days to 50% flowering, days to maturity and dry fodder. Positive correlations were observed between green fodder yield and other traits, indicating their potential for enhancing yield. Principal component analysis identified four principal components that accounted for 69.87% of the total variation. Cluster analysis categorized the genotypes into two main clusters and six sub-clusters. Frost damage assessment was conducted at tillering stage after the snow melted in late January 2021 and 2022 using cold tolerance rating scale and subsequently tested for chilling injury through an electrolyte leakage test. From field and lab data analysis, five most promising cold tolerant, nutritious and high-yielding genotypes were identified. These genotypes have significant potential for utilization in future breeding programmes to improve cold tolerance in cultivated oats within the Kashmir valley thus promoting agricultural productivity and sustainability. The outcomes also provide valuable insights into the genetic variation, heritability, genotype-by-environment interactions, correlations and cold tolerance of oat genotypes in Kashmir.

Attention deficit hyperactivity disorder (ADHD) is a highly prevalent neurodevelopmental disorder occurring in approximately one in twenty young people in Ireland, and in one-third of those attending Irish Child and Adolescent Mental Health Services (CAMHS). It is important to treat ADHD, as un/poorly treated ADHD is associated with a raft of negative health and socio-economic outcomes. Effective interventions for ADHD are available, and the use of standardised, evidence-based pathways for assessment and management of ADHD optimises outcomes. Despite this, there is no national standardised clinical pathway for assessment and treatment of ADHD in Ireland. ADMiRE, the first public healthcare specialist service for children and adolescents in Ireland, has developed a strongly evidence-based, efficient, effective and safe clinical pathway for assessment and management of ADHD. This paper describes the ADMiRE Clinical Pathway and references ADMiRE resources that are available to other services.

Relative to the numerous studies focused on mammalian schistosomes, fewer include avian schistosomatids particularly in the southern hemisphere. This is changing and current research emerging from the Neotropics shows a remarkable diversity of endemic taxa. To contribute to this effort, nine ducks (Spatula cyanoptera, S. versicolor, Netta peposaca), 12 swans (Cygnus melancoryphus) and 1,400 Physa spp. snails from Chile and Argentina were collected for adults and larval schistosomatids, respectively. Isolated schistosomatids were preserved for morphological and molecular analyses (28S and COI genes). Four different schistosomatid taxa were retrieved from birds: Trichobilharzia sp. in N. peposaca and S. cyanoptera that formed a clade; S. cyanoptera and S. versicolor hosted Trichobilharzia querquedulae; Cygnus melancoryphus hosted the nasal schistosomatid, Nasusbilharzia melancorhypha; and one visceral, Schistosomatidae gen. sp., which formed a clade with furcocercariae from Argentina and Chile from previous work. Of the physid snails, only one from Argentina had schistosomatid furcocercariae that based on molecular analyses grouped with T. querquedulae. This study represents the first description of adult schistosomatids from Chile as well as the elucidation of the life cycles of N. melancorhypha and T. querquedulae in Chile and Neotropics, respectively. Without well-preserved adults, the putative new genus Schistosomatidae gen. sp. could not be described, but its life cycle involves Chilina spp. and C. melancoryphus. Scanning electron microscopy of T. querquedulae revealed additional, undescribed morphological traits, highlighting its diagnostic importance. Authors stress the need for additional surveys of avian schistosomatids from the Neotropics to better understand their evolutionary history.

Marginalisation is a multilevel phenomenon in society depriving people from essential rights, resources, and opportunities. Street-outreach services in the Netherlands, like social street work (SSW), support these marginalised people in fostering their participation in society as an answer to their marginalised position in society. We followed 927 clients in SSW over an eight-month period. Clients filled in a questionnaire at three timepoints. We examined whether clients’ perceived belongingness, self-esteem, strengths, and informal support (outcome measures) were associated with the working relationship, over time. Results showed the establishment of a working relationship with clients at all three timepoints. An evolving working relationship was associated with an increase in clients’ perceived belongingness, self-esteem, strengths, and informal support over time. This study showed the ability of workers to establish a working relationship with clients in their living environment and underscored the necessity of establishing a working relationship in street-outreach services to foster clients’ participation in society. This study encourages policymakers to reflect on current street-outreach services, to deviate from demanding short-term and measurable results from professionals’ efforts, and to opt for a better fit between performance and financing conditions and daily practices of street-outreach services.