Let $\overline {M}(a,c,n)$ denote the number of overpartitions of n with first residual crank congruent to a modulo c with $c\geq 3$ being odd and $0\leq a<c$. The central objective of this paper is twofold: firstly, to establish an asymptotic formula for the crank of overpartitions; and secondly, to establish several inequalities concerning $\overline {M}(a,c,n)$ that encompasses crank differences, positivity, and strict log-subadditivity.

The Antarctic Treaty System has put in place international agreements to provide comprehensive protection of the Antarctic environment. Despite this high degree of protection, human presence on the continent has resulted in environmental contamination, particularly at locations established prior to the development of the more stringent codes of conduct in recent decades. Rehabilitation of legacy contaminated sites is a priority for environmental management, and a framework for such efforts has been established. In this contribution, we re-evaluate the rehabilitation of the site of the former Vanda Station, a New Zealand outpost occupied from 1969 to 1991. We describe the design and implementation of the restoration, which included the removal of many tonnes of contaminated soils and groundwater, along with the post-action monitoring of the site. Our goal is to determine where challenges to the use of recent guidelines would have arisen. We found that while guidelines on clean-up of contaminated sites in Antarctica are valuable, challenges to implementation remain. These largely reflect a lack of understanding of the consequences of contamination on Antarctic ecosystems and the trajectory of natural rehabilitation. We present recommendations on how to address some of these challenges.

Insect odorant-binding proteins (OBPs) are the key proteins in insect olfactory perception and play an important role in the perception and discrimination of insects. Frankliniella occidentalis is a polyphagous pest and seriously harms the quality and yield of fruits, flowers and crops worldwide. Therefore, the discovery of OBPs has greatly improved the understanding of behavioural response that mediates the chemoreception of F. occidentalis. To identify the OBP gene of F. occidentalis and its sequence and expression, rapid amplification cDNA ends (RACE) and qRT-PCR reaction system were performed. The results showed that the sequence of FoccOBP9 gene was 846 bp and the reading frame was 558 bp, encoding 185 amino acid residues, a 3′ non-coding region of 195 bp and a 5′ non-coding region of 93 bp.The molecular weight of the protein was about 20.08 kDa, and the isoelectric point was 8.89. FoccOBP9 was similar to AtumGOBP and CnipOBP2 (30%), followed by BdorGOBP, DficGOBP, DsuzGOBP, AalbOBP38, CmarOBP6 and SexiOBP. Phylogenetic analysis of the FoccOBP9 demonstrated that the FoccOBP9 had a relatively close evolutionary relationship with SgreOBP1, AtumGOBP, HeleOBP3, CbowOBP17, CnipOBP2 and CpalOBP2. The prediction of secondary structure showed that FoccOBP9 protein contained 135 amino acid residues forming α-helix, 91 amino acid residues forming β-sheets and 24 amino acid residues forming β-turning. However, three-dimensional structure prediction showed that the FoccOBP9 protein skeleton was composed of six α-helices and the loops connecting these helices. Dynamic observation of the three-dimensional structure revealed that five α-helices (α1, α2, α4, α5, α6) were found in the structure. The expression profiles analysis revealed that FoccOBP9 are highly abundant in antenna significantly, followed by the head and belly, and almost no expression in the chest and foot. Therefore, the identification and analysis of OBP may be useful for monitoring and limiting the damage of F. occidentalis.

The Republic of Sakha (Yakutia) faces serious demographic challenges. One of the most important among them is the imbalance of population flows within internal migration. This paper examines the patterns of internal migration in the Republic, based on the distribution of municipal districts (uluses) by economic zones designated by the authorities for administrative purposes. The six most common indices characterising the intensity of migration of the population were used for the analysis. The homogeneity of Yakutia’s districts according to these indices was tested using the van der Waerden test. The article reveals that the intensity of migration in Yakutia has increased since 2011. The financial crisis of 2008–2009 and the COVID-19 pandemic had a significant but temporary impact on internal migration in Yakutia. Only Yakutsk has experienced population growth due to internal migration throughout the period studied. The intensity of migration in the Arctic uluses was not statistically different from central and eastern uluses, but differed from the most economically developed districts in southern and western Yakutia. The Republic was homogeneous with respect to the balance of migration inflows and outflows, but there was considerable heterogeneity in terms of the impact of migration on the size of the population.

This article develops a novel argument that God’s existence would greatly increase our prospects for meaning in life. The key idea is that if God exists, He stands in certain relations to the world that would confer value upon it. For instance, God would be its creator and sustainer. The world would thus gain value in much the way that relics gain value by their links with historical persons and events. And crucially, as a result of this infusion of value, our lives go better because the things we engage with matter more.

The topological structure of ‘mean dichotomy spectrum’ is shown in this article, as an extension of Sacker–Sell spectrum and non-uniform dichotomy spectrum. With regard to mean hyperbolic systems, the coexistence of expansion and contraction behaviours can lead to non-hyperbolic phenomena during evolution process. To be precise, distinct from uniform and non-uniform hyperbolic cases, error hyperbolic degree $\varepsilon(t,\tau)$ is vital to depict the spectral manifolds. As application, the reducibility theorem for mean hyperbolic systems is provided to deduce block diagonalization.

The ability to detect and monitor errors enables us to maintain optimal performance across tasks. One neurophysiological index of error monitoring is the error-related negativity (ERN), a fronto-central negative deflection peaking between 0 and 150 ms following an erroneous response. While the developmental literature has illustrated age-related differences in the ERN and its association with anxiety, the literature has mainly focused on the between-person differences of the ERN. Our study examined the within-person variations of the ERN in 115 community-dwelling 9- to 12-year-olds (66 girls; mean age/SD = 11.00/1.16 years). Participants completed an EEG Go/No-Go task and reported their anxiety symptoms. Multilevel growth analyses yielded significant within-person, curvilinear changes in the ERN throughout the task. Youths’ trial-level ERN increased (i.e., became more negative) with early errors, but decreased with subsequent errors. This curvilinear pattern was evident in older, but not younger, youths. Age also interacted with anxiety symptoms: younger youths with higher anxiety showed a continuous increase in the ERN throughout the task, whereas older youths with higher anxiety showed an initial increase followed by a decline in the ERN. Our study contributed novel evidence for the development of the ERN and the underlying mechanisms of the ERN-anxiety relationship that cannot be captured by between-person approaches.

This paper constructs the intellectual histories of learned societies in Ghana to illuminate African agency in pursuing knowledge production and dissemination. Academics and politicians founded some of Africa’s first scientific societies in Ghana. Previous scholarship on scientific research and higher education in Africa has overlooked the role of disciplines-based learned societies and national academies. This paper contributes to that literature using a historical comparative approach to construct the histories of learned societies that emerged during the colonial and postcolonial periods to understand how such scientific associations contributed to research productivity. I advance two arguments based on case studies of three scientific societies. First, there is linearity in the evolution of learned societies. Second, the institutionalization of scientific communities along interdisciplinary and transdisciplinary lines provided flexibility and enabled learned associations to contribute relevant knowledge to the “developmental state” that the political leaders were constructing.

A nontrivial element of a group is a generalized torsion element if some products of its conjugates is the identity. The minimum number of such conjugates is called a generalized torsion order. We provide several restrictions for generalized torsion orders by using the Alexander polynomial.

In this paper, we first introduce the concept of symmetric biderivation radicals and characteristic subalgebras of Lie algebras and study their properties. Based on these results, we precisely determine biderivations of some Lie algebras including finite-dimensional simple Lie algebras over arbitrary fields of characteristic not $2$ or $3$, and the Witt algebras $\mathcal {W}^+_n$ over fields of characteristic $0$. As an application, commutative post-Lie algebra structure on the aforementioned Lie algebras is shown to be trivial.

This paper explores the reasons that divorce petitions by trafficked women in China were denied in courts in the wake of the chained woman incident. The author collected and examined divorce verdicts involving trafficked women from China Judgements Online. Among 100 unique cases, 87 were denied in their first attempts. Most of these cases were treated in the same way as regular divorce cases, with trafficking allegations either blatantly ignored or dismissed as irrelevant. The author argues that the systematic denials and ignoring of trafficking allegations is enabled by a hegemonic legal consciousness within the Circuit of Trafficking that includes not only parties directly engaged in trafficking activities, but also state actors such as the judges and legislators who prioritise “family” preservation and social stability over the rights and well-being of trafficked women. Without addressing and changing this hegemonic legal consciousness, any reform, if it should take place, would be rendered futile in practice.

Mosquitoes, particularly Aedes aegypti, pose significant public health risks by transmitting diseases like dengue, zika and chikungunya. Bacillus thuringiensis var. israelensis (BTI) is a crucial larvicide targeting mosquitoes while sparing other organisms and the environment. This study evaluated the effects of sublethal BTI doses on Ae. aegypti larvae regarding mortality, development, adult emergence and size, using a wide-area spray application in an urban neighbourhood. Laboratory experiments with four BTI concentrations (0, 0.008, 0.02 and 0.04 ppm) assessed compensatory and over compensatory responses. The spray achieved over 90% larval mortality within 48 h, but accumulating sublethal doses could trigger compensatory and over compensatory effects, enhancing the fitness of survivors. A dose–response relationship was evident, with higher BTI concentrations leading to increased mortality, reduced longevity and fewer pupae. BTI exposure also skewed the sex ratio towards males and altered adult sizes, potentially affecting population dynamics and vectorial capacity. These findings highlight the effectiveness of BTI in Ae. aegypti control and the importance of understanding compensation, overcompensation and density-dependent effects. While wide-area BTI applications can reach inaccessible breeding sites and offer potent mosquito control, careful consideration of ecological and evolutionary consequences is crucial.