Accurately estimating large-area crop yields, especially for soybeans, is essential for addressing global food security challenges. This study introduces a deep learning framework that focuses on precise county-level soybean yield estimation in the United States. It utilizes a wide range of multi-variable remote sensing data. The model used in this study is a state-of-the-art CNN-BiGRU model, which is enhanced by the GOA and a novel attention mechanism (GCBA). This model excels in handling intricate time series and diverse remote sensing datasets. Compared to five leading machine learning and deep learning models, our GCBA model demonstrates superior performance, particularly in the 2019 and 2020 evaluations, achieving remarkable R², RMSE, MAE and MAPE values. This sets a new benchmark in yield estimation accuracy. Importantly, the study highlights the significance of integrating multi-source remote sensing data. It reveals that synthesizing information from various sensors and incorporating photosynthesis-related parameters significantly enhances yield estimation precision. These advancements not only provide transformative insights for precision agricultural management but also establish a solid scientific foundation for informed decision-making in global agricultural production and food security.

In this paper a class of nonlocal diffusion equations associated with a p-Laplace operator, usually referred to as p-Kirchhoff equations, are studied. By applying Galerkin’s approximation and the modified potential well method, we obtain a threshold result for the solutions to exist globally or to blow up in finite time for subcritical and critical initial energy. The decay rate of the L 2 norm is also obtained for global solutions. When the initial energy is supercritical, an abstract criterion is given for the solutions to exist globally or to blow up in finite time, in terms of two variational numbers. These generalize some recent results obtained in [Y. Han and Q. Li, Threshold results for the existence of global and blow-up solutions to Kirchhoff equations with arbitrary initial energy, Computers and Mathematics with Applications, 75(9):3283–3297, 2018].

In this article, we extend the 9 - intersection matrix to 27 - intersection matrix on the basis of RCC8 relations, propose 27 - intersection model between two disjoint regions and a simple region. Giving the algorithm, 31 kinds of topological relations between two disjoint regions and a simple region by specific procedure, and give schematic diagrams of the 31 kinds of topological relations, verifying 31 kinds of topological relations are achievable. In order to further research the topological relations between two disjoint regions and a simple region, in this article we have completed the reasoning for topological relations between two disjoint regions and a simple region, and given the conceptual neighborhood graph. By comparison of related work, we can draw a conclusion that the 27 - intersection model is superior to the expressive power of the 8-intersection model. Through the representation model of topological relations established in this article, we can predict the rainfall situation on two areas, and give the probability of rainfall in different regions.