Along with the aging of the population and miniaturization of family structure, the problem of the left-behind elderly has become more and more prominent in China. According to the Report on the family development in China (2015) released by the National Health Commission of the People’s Republic of China, left-behind elderly people account for half of the total number of the elderly, of whom 10% live alone. The left-behind elderly not only suffer physiological obstacles such as body function decline, but also face a lack of support at the material level and loneliness at the spiritual level, which greatly affects their quality of life, accounting for their lower life satisfaction than that of the ordinary elderly. The rural areas of Sichuan Province are relatively backwards in terms of economic level and have limited pension security. Therefore, the left-behind elderly in rural areas are confronted with more complicated and severe pension problems compared with those in urban areas. Meanwhile, limited by economic and regional factors, a large number of rural labor forces in Sichuan Province have transferred to cities. These long-time migrant workers cannot provide material, spiritual and life care support for their left-behind parents in rural areas in a timely fashion, which changes their filial piety behaviors, and this affects the life satisfaction of the rural left-behind elderly. Therefore, it is necessary to understand the living conditions of empty-nest elderly and their children’s filial piety in rural areas of Sichuan province in order to verify the influence mechanism of filial piety on the life satisfaction of the elderly, and to explore how to improve the rural empty-nest elderly’s life satisfaction, enabling the elderly to live a healthy and happy life.

Amid the exponential growth of streaming data and rising demands for real-time decision-making, Online Convex Optimization (OCO) has emerged as a foundational framework for sequential data processing in dynamic environments. This survey presents a systematic review of recent evolutionary and adaptive OCO strategies, offering a detailed taxonomy that classifies algorithms according to their constraint-handling mechanisms and environmental feedback. The analysis first examines Constrained OCO, elucidating the trade-offs between computational efficiency and theoretical guarantees across projection-based methods, projection-free Frank–Wolfe variants, and general convex optimization approaches. It then explores the Unconstrained OCO landscape, emphasizing the shift from parameter-dependent methods to fully adaptive, parameter-free algorithms capable of handling unknown comparator norms and gradient scales. Furthermore, the study synthesizes state-of-the-art applications in power systems, network communication, and quantitative finance, bridging theoretical OCO models with robust engineering solutions. The paper concludes by outlining critical open challenges and future research directions, such as the integration of OCO with deep learning, non-convex optimization, and robustness against adversarial corruptions in data-intensive scenarios.

Bioretention cells are an important facility to solve the hydrological and non-point pollution problems in urban areas, especially phosphorus. In this paper, ceramsite composite was made from coal ash and modified by nano-iron through coprecipitation and reduction, which was used to remove the phosphorus in the water. The results of the characteristics of the ceramsite composite using scanning electron microscope showed that the surface of the ceramsite loaded with nano-iron became rougher and the iron nanoparticles were uniformly distributed on the surface, and there was no obvious agglomeration of nano-iron particles. The loading effect was good and the activity of the ceramsite was greatly improved. The results from the static and dynamic continuous experiments indicated that the modified ceramsite with nano-iron had a good removal effect on phosphorus, and the removal rate reached over 99%. The results of this study can provide a new way for the resource utilization of coal ash, and also inspires a new idea for the improvement of filler in bioretention facilities.