In this paper, we express the generating function of a combination of cranks of partitions that belong to congruence classes 3, 4, 5, 6, and 7 modulo 15, in terms of the Eisenstein series. Our results rely on the observation that the generating function of the combination we consider is a weight 1 modular form on Γ0(225) with the non-trivial modulo 3 primitive Dirichlet character. We obtain the modularity result by analyzing the transformation properties of related Klein forms. The main results are proven using the fact that the corresponding space is generated by Eisenstein series.
Land management practices dictate soil physico-chemical and biological functions, and consequently, the agroecological benefits of soils. While several studies exist detailing the effects of cover crops on soil health parameters in annual systems, there is no clear understanding of microbial responses under perennial systems, especially after conversion to annual systems. A 20-year perennial fescue (Schendonorus arundinaceus) field was converted to annual systems including two levels of cover crops (cover crop vs no cover crop) and two levels of tillage (tillage vs no tillage). The cover crop included a mix of winter wheat (Triticum aestivum) and crimson clover (Trifolium incarnatum), while the tillage included disc plowing. Three and four years after conversion, soil samples were collected from no-till with cover crop (NT-CC), no-till with no cover crop (NT-NC), tillage with cover crop (Till-CC), and tillage with no cover crop (Till-NC) plots. Additional samples were also collected from an adjacent field under perennial fescue grass (PER). Soil physico-chemical properties were greater (p < 0.05) under PER and NT-CC than other management practices evaluated. As a result, total microbial biomass and the composition of microbial community were greater under PER and NT-CC than other management practices. Four years after conversion, the Gr- bacteria and fungi populations under PER were 49% and 59% greater than the average of all CC, and 51% and 133% greater under the average of all tillage managements, respectively. Further, the predato:prey ratio was 38% greater under PER than Till-CC and Till-NC managements. While a conversion from perennial to annual systems can result in soil health parameter degradation, NT-CC is a better annual alternative to perennial systems than other annual practices evaluated.
This paper develops a theoretical model to study how cross-country productivity asymmetry affects the endogenous formation of global free trade. The main theoretical prediction is that (i) when productivity levels are sufficiently similar, the equilibrium is global free trade; and (ii) when productivity levels are sufficiently asymmetric, the equilibrium outcome is the status quo regime. We empirically confirm the main theoretical prediction using panel data from 195 & times; 194 country pairs, along with information on all FTAs formed in the world from 1950 to 2017. The empirical results suggest that country pairs with higher productivity asymmetry are less likely to sign a reciprocal trade agreement. Therefore, this paper rationalizes the inclusion of productivity differences in empirical studies on the formation of trade agreements.
The metamorphosis of aquatic emergent insects results in energetic subsidies that connect aquatic and terrestrial ecosystems, providing important resources to riparian consumers but also serving as a pathway for the transfer of bioaccumulative and biomagnifying contaminants. The transfer of contaminants can put riparian predators at risk of exposure and negative health effects; therefore, understanding the mechanisms of emergent-insect contaminant flux is important for ecological risk assessments. Metamorphosis can affect the concentration of some chemical contaminants in larvae relative to adult insects. However, ecological risk assessments often do not consider life stage in the use of aquatic insects. Additionally, foodweb tracers (e.g., stable isotopes) are commonly used in risk assessments, but the influence of metamorphosis on these tracers is not well studied. In this study, we investigated whether metamorphosis was associated with changes to commonly used foodweb tracers in mayflies. We compared stable isotopes, polyunsaturated fatty acid profiles, and body composition in multiple life stages of the model laboratory mayfly species Neocloeon triangulifer (McDunnough, 1931) and field-collected mayflies (order Ephemeroptera, family Heptageniidae) to evaluate life-stage effects under controlled and natural conditions and across species. In laboratory-reared mayflies, delta 15N, %N, and arachidonic acid increased with metamorphosis, but in field-collected mayflies, delta 15N decreased and polyunsaturated fatty acid profiles did not differ. Our results indicate that metamorphosis has an effect on foodweb tracers in both laboratory and field-collected mayflies, which should be considered when using mayflies, or potentially other emergent aquatic insects, in calculations connected to ecological risk assessments.
Sentence repetition tasks have been shown to be sensitive indicators of developmental language disorder (DLD), with prior work demonstrating strong group-level differences between children with DLD and typically developing peers. However, less is known about how sentence repetition performance relates to broader language difficulties among students already identified with dyslexia. Dyslexia is characterized primarily by word-level reading and spelling difficulties, yet many students with dyslexia also exhibit oral language weaknesses consistent with DLD, which carry important implications for academic outcomes. The present pilot study examined whether sentence repetition performance was associated with indicators of broader language difficulty among students with dyslexia. Participants were 22 fourth-grade students attending a specialized school for language-based learning disabilities, all of whom carried a diagnosis of dyslexia. Sentence repetition performance was examined in relation to students’ current or recent qualification for speech-language services, used as a proxy indicator of broader language difficulty. Students receiving speech-language services demonstrated substantially lower sentence repetition scores than their peers with dyslexia who were not receiving services, with a large group difference observed. Logistic regression was used descriptively to illustrate how sentence repetition performance corresponded to observed service-status groupings in this small sample. Findings should be interpreted as preliminary and associative, consistent with the exploratory nature of the study. Results suggest that sentence repetition performance may warrant further investigation as a potential indicator of broader language vulnerability within dyslexia-identified populations and highlight the need for larger, prospective studies examining oral language assessment in students with dyslexia.
