Single-metal phase ternary phosphorus/selenide materials have shown promise as high-capacity anodes for advanced sodium-ion batteries (SIBs) because of their substantial reversible capacity. However, their utilization has been hampered by issues such as sluggish kinetics and material pulverization during charge/discharge cycles, leading to inadequate rate capability and lifespan. To address these challenges, herein, N-doped graphene aerogel (NGA) compounding ternary FePSe3 to form a sponge-like heterostructured architecture FePSe3@NGA is synthesized through a combined phosphatization/selenation method and hydrothermal approach. The composite is probed as an anode for SIBs. Profiting from the enhanced electrical conduction and Na+ diffusion kinetics together with efficient mitigation of volume deformation, the FePSe3@NGA presents excellent sodium storage performance. The FePSe3@NGA delivers 302 mAh g−1 after 100 cycles at 0.1 A g−1, and 156 mAh g−1 after 600 cycles at 1 A g−1, with a capacity retention of 72
Fluorescence molecular tomography (FMT) is a promising medical imaging technique that enables non-invasive, specific, and sensitive detection of the fluorophore. However, multiple-target resolving remains a challenge in FMT. Its key issue is how to determine the number of targets, which is difficult to obtain in practical applications. To address this issue, a three-way clustering algorithm based on shadowed sets is proposed in this work. It not only provides the appropriate number of clusters automatically but also determines the partition thresholds. First, we have defined a shadowed set similarity to quantify the similarity between fuzzy information samples. Second, based on the concept of shadowed set similarity, the intra-class similarity and inter-class similarity are introduced to quantify the change of the relationship between the sample and the clusters. Furthermore, an improved clustering validity index ( C V I) is created to measure the clustering performance. At the same time, the optimal cluster number is determined according to the C V I. Finally, the proposed method has been applied to FMT for adaptively determining the number of fluorescent targets. The experimental data of FMT indicate that the proposed algorithm can accurately determine the number of fluorescent targets from the effective reconstruction results. University of California Irvine (UCI) datasets further demonstrated the potential of the method.
This article aims to investigate whether there exist infinitely many primes p such that [alpha(1)p(1)(C) + alpha(2)p(2)(C) + beta] is also a prime for almost all irrationals alpha(1) > 0 and alpha(2) > 0 (in the sense of Lebesgue measure). Our result provides an affirmative answer to this question by utilizing elementary and analytic methods, especially the division trick and estimates of exponential sums.
Graph neural networks (GNN) have shown strong performance in node classification tasks, yet most existing models rely on uniform or shared weight aggregation, lacking flexibility in modeling the varying strength of relationships among nodes. This paper proposes a novel graph coupling convolutional model that introduces an adaptive weighting mechanism to assign distinct importance to neighboring nodes based on their similarity to the central node. Unlike traditional methods, the proposed coupling strategy enhances the interpretability of node interactions while maintaining competitive classification performance. The model operates in the spatial domain, utilizing adjacency list structures for efficient convolution and addressing the limitations of weight sharing through a coupling-based similarity computation. Extensive experiments are conducted on five graph-structured datasets, including Cora, Citeseer, PubMed, Reddit, and BlogCatalog, as well as a custom topology dataset constructed from the Open University Learning Analytics Dataset (OULAD) educational platform. Results demonstrate that the proposed model achieves good classification accuracy, while significantly reducing training time through direct second-order neighbor fusion and data preprocessing. Moreover, analysis of neighborhood order reveals that considering third-order neighbors offers limited accuracy gains but introduces considerable computational overhead, confirming the efficiency of first-and second-order convolution in practical applications. Overall, the proposed graph coupling model offers a lightweight, interpretable, and effective framework for multi-label node classification in complex networks.
Farmland fragmentation and green productivity are pivotal challenges in global agriculture, especially in ecologically fragile river basins where farming is crucial and the environment is precarious. Yet, the intensity and pathway through which county-level fragmentation undermine green productivity remain largely unexplored. This study examines 447 counties in the Yellow River basin using the CNLUCC dataset to calculate farmland fragmentation index (FFI). Utilizing panel data from 2000, 2005, 2010, 2015, and 2020, we develop an assessment framework of farmland green productivity (FGP), which is estimated using a super-efficiency SBM model. Based on the "quantity-spatial" scale effects and Environmental Kuznets Curve (EKC) theory, this study develops a theoretical model of FFI's impact on FGP and conducts a comparative statics and green elasticity analysis. Furthermore, fixed effects, instrumental variable (IV), mediation, and moderation models are applied to empirically dissect the impact and underlying mechanism of FFI on FGP, complemented by heterogeneity analysis. Our results reveal that: (1) FFI exerts a significant negative influence on FGP, a finding that holds robust across various tests and remains consistent even when road network is used as an IV to address endogeneity. Specifically, a one-unit increase in FFI corresponds to a 0.438-unit decline in FGP, equivalent to a 69 % decrease; (2) the adverse impact of fragmentation on FGP varies markedly across location, topography, development statuses, and fragmentation intensity. In particular, rugged topography exacerbates the negative effect, especially in mountainous areas, while under high grain cropping structures, fragmentation more strongly suppresses FGP in plains by impeding mechanization and resource consolidation; (3) mechanism analysis indicates that FFI diminishes FGP primarily by shifts toward non-grain cropping structures, curtailing mechanization intensity, and escalating agrochemical inputs. Additionally, larger farm size serves to buffer the negative impacts of fragmentation. Furthermore, fragmentation delays the arrival of the EKC turning point. In light of these findings, policy measures should prioritize farmland consolidation, the optimization of cropping structures, the adoption of green technologies, and the expansion of farm size to foster agricultural sustainable intensification and mitigate the deleterious effects of fragmentation on green productivity.
