The recession cone and recession function are very important research objects in Convex Analysis. They have extensive applications in the optimization theory. Firstly, we study the properties of the recession cone and recession function. The positive homogeneity and subadditivity of recession function are mainly discussed. And the different methods are considered to prove these properties. Secondly, we discuss the unboundedness of the convex sets and convex functions by using recession cone and recession function.

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.