Nontrivial solutions of singular two-point boundary value problems with sign-changing nonlinear terms

AbstractThe singular two-point boundary value problem−u″(t)=h(t)f(u(t)),t∈(0,1);u(0)=u(1)=0 is considered under some conditions concerning the first eigenvalue corresponding to the relevant linear problem, where h is allowed to be singular at both t=0 and t=1. Moreover, f:(−∞,+∞)→(−∞,+∞) is a sign-changing function and not necessarily bounded from below. By computing the topological degree of an completely continuous field, the existence results of nontrivial solutions are established

Long-Term N Addition, Not Warming, Increases Net Ecosystem CO\u3csub\u3e2\u3c/sub\u3e Exchange in a Desert Steppe in Northern China

Grasslands cover a major part of the global terrestrial area and provide important ecosystem functions such as sequestration of carbon (C). Desert steppes are unique ecosystems with properties in between desert and grasslands. They are considered to be vulnerable ecosystems that are at risk of desertification due to global change. To provide a robust prediction of the effect of climate warming and increased nitrogen (N) deposition on desert steppe, long-term studies that capture the annual variation in precipitation are needed. We conducted a 12-year field experiment in a desert steppe which showed that warming did not change ecosystem C exchange whereas N addition increased ecosystem C storage. Moreover, warming did not change total aboveground biomass, mainly due to the contrasting responses of C4 and C3 plants, especially in the presence of additional N. Therefore, our study predicts that warming do not necessarily lead to degradation of the desert steppe and N addition may have a positive effect on CO2 sequestration, providing a negative feedback on climate change. However, these global change drivers do alter vegetation composition in the desert steppe, which can have consequences on a diversity of ecosystem functions

Effects of Different Grazing Intensities on Grasshopper Communities in \u3cem\u3eStipa breviflora\u3c/em\u3e Desert Steppe

As a common method of grassland management, grazing plays an important role in grassland conservation. Grasshoppers and large herbivores are integral parts of grassland biodiversity and food webs. However, to some extent there is still room for further research on how grasshoppers cope with grazing by large herbivores. A field grazing experiment in Stipa breviflora desert steppe in Inner Mongolia, China to investigate the effects of sheep grazing intensity on the abundance and richness of locust population and community. The grazing experiment started in 2004, and the grasshopper population and community were investigated in 2021. The results showed that: Grazing results in the change of dominant species of grasshopper in desert steppe from the C.abbreviatus to the O.asiaticus. Grazing intensity increases the abundance of dominant species, thus increasing the risk of grasshopper outbreaks. Our results suggest that light grazing by sheep is a beneficial management practice to maintain locust species diversity, but at the same time keep the abundance lo

Interactions Between Foraging Behaviour of Herbivores and Grassland Resources in the Eastern Eurasian Steppes

In rangeland areas such as the eastern Eurasian steppes (Mongolia and China), foraging behaviour is influenced by plant or vegetation properties with high heterogeneity. Until recently foraging theory has not accounted for the foraging process or ingestive behaviour. Existing theories on foraging behaviour need to evolve and begin to coalesce, and combine with observations or manipulative experiments. Plant and patch properties such as diversity and height influence animal foraging behaviour (related to foraging process or diet selection) in heterogeneous steppes. Stocking rate is the most important management factor for grazing or vegetation management, and determining the optimal stocking rate in steppes depends upon variable annual forage production, vegetation regrowth and animal production targets

Interactions between Foraging Behaviour of Herbivores and Grassland Resources in the Eastern Eurasian Steppes

Key points 1. In rangeland areas such as the eastern Eurasian steppes (Mongolia and China), foraging behaviour is influenced by plant or vegetation properties with high heterogeneity. 2. Until recently foraging theory has not accounted for the foraging process or ingestive behaviour. Existing theories on foraging behaviour need to evolve and begin to coalesce, and combine with observations or manipulative experiments. 3. Plant and patch properties such as diversity and height influence animal foraging behaviour (related to foraging process or diet selection) in heterogeneous steppes. 4. Stocking rate is the most important management factor for grazing or vegetation management, and determining the optimal stocking rate in steppes depends upon variable annual forage production, vegetation regrowth and animal production targets

Deformable Convolutional Networks

Convolutional neural networks (CNNs) are inherently limited to model geometric transformations due to the fixed geometric structures in its building modules. In this work, we introduce two new modules to enhance the transformation modeling capacity of CNNs, namely, deformable convolution and deformable RoI pooling. Both are based on the idea of augmenting the spatial sampling locations in the modules with additional offsets and learning the offsets from target tasks, without additional supervision. The new modules can readily replace their plain counterparts in existing CNNs and can be easily trained end-to-end by standard back-propagation, giving rise to deformable convolutional networks. Extensive experiments validate the effectiveness of our approach on sophisticated vision tasks of object detection and semantic segmentation. The code would be released