Usually in the study of limit problems, will encounter more complex problems, in this paper, we discuss how to use the concept of equivalent infinitesimal better limit operation. At the same time, in the process of research, we re-explore the proof of Taylor's formula, and find that some functions have a similar expansion form to Taylor's formula, that is, 'fractional expansion'. It is also found that after the linear combination of Taylor expansion and fractional expansion, the obtained expansion is more accurate, which helps us to have a better understanding of the approximation of function expansion.

This study, through the method of canonical correlation analysis, revealed significant correlations between various dimensions of learning attitudes of students and various dimensions of teacher knowledge. An analysis of data from a group of 221 high school students showed that teacher knowledge of teaching content, theoretical knowledge, and teaching practice and classroom management significantly impact learning attitudes of students. Specifically, teacher knowledge of teaching content plays a crucial role in promoting students' behavioral inclination to learn chemistry, teachers' theoretical knowledge significantly enhances students' liking for chemistry laboratory courses, while teachers' teaching practice and classroom management have a suppressive effect on students' evaluative beliefs about school chemistry. The results of this study provide effective guidance for both the theory and practice of high school chemistry education.

This article explores the properties of Fibonacci sequences and their widespread applications.

Effective harvesting strategies are crucial for maximizing annual catch and ensuring the sustainability of lobster (Homarus americanus) farming. This paper presents a nonlinear objective programming model to optimize harvesting intensity based on lobster life cycle dynamics and harvesting characteristics. We model the population dynamics of 1-4 year-old lobsters using differential equations to account for natural mortality, spawning, and harvesting effects. Solving the model with LINGO 12.0, we determine that the optimal harvesting intensity coefficient is 17.36, which maximizes annual catch to 3.88 × 10¹⁰ grams. Results indicate that maintaining harvesting intensity around this optimal value balances economic benefits and population stability, ensuring sustainable farm operations.

Disaster Risk Management benefits from innovative techniques including AI and Multi Sensor Fusion. The Firefguard Approach uses such technologies to improve the Wildfire Management works in Saxony, Eastern Germany by supporting standing efforts in Early Warning, Disaster Response and Monitoring. Unmanned Aerial Systems (UAS) play a vital role in providing real-time information via a 5G network to a central information management system that delivers geospatial information to response teams. This study highlights the potential of combining UAS, AI, geospatial solutions and existing data for real-time wildfire monitoring and risk assessment systems.

Land use as for human-circumstance interaction is as we all know changed the global land surface sharply and continuously. Farmland abandonment is the phenomenon of going extreme of marginal of land use, which exert positive and negative impacts on our living circumstances. In order to map the extent of farmland abandonment of Zhejiang Province, we try to use the geo-big data analysis platform to perform the massive data preprocessing and map the extent of farmland abandonment of the study area based on multi-source land use and land cover data. Then we execute landscape pattern analysis using landscape pattern analysis software and spatial auto-correlation (Moran's I) analysis based on ArcGIS and Fragstats software. We found that the area of farmland is about 16.32% on account of all land use types, which is 1.89104 km2. While the whole area of FA is 1.72 × 108 m2, and the farmland abandonment ratio is 1.65%. AF's area is about 1.95 × 109 m2, and the continuous cultivation ratio is 18.69%. The landscape fragmentation, landscape aggregation and landscape diversity of FA, AF and FL are different. At the same time, the spatial auto-correlation of FA and AF are dominant high congregation and low discrete. At last, we compared our calculated results with the existed research results which demonstrate our research does scientific convincible. We also make futural prospects prediction and show the research deficiency as well as bring out some policy implications based on our research, which means build proper land use management regulation and decrease the farmland abandonment on account of the premise of suitable land use policies.