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.

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.

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.

This paper reconceives zero not as a mere absence but as an axis unifying positive and negative infinities. We introduce the notion of Unzero (Ø) to emphasize zero’s active role in mathematical structure. By analyzing limits of the form n/m as m→0⁺ and m→0⁻, we show that Unzero naturally serves as a pivot between divergent magnitudes. We formalize Unzero within a minimal algebraic extension of the real numbers, compare it with projective and non standard frameworks, and explore illustrative examples in analysis and geometry. This unified perspective clarifies longstanding ambiguities around division by zero, offers a coherent notation respecting classical limits, and suggests avenues for further algebraic and topological development.

An experiment was conducted to assess the effect of psychoenergetic energy in litchi as positive and negative thoughts using a simple meditation technique at ICAR-NRC on Litchi, Muzaffarpur. The plant produced 24.75 g of fruit given positive energy, while the plant with negative thought energy produced 22.12 g of fruit. The fruit and seed weight increased by 11.88% and 13.63%, respectively, due to positive energy. The number of fruit retentions increased by 23.77% due to positive energy. Anthocyanin content in pericarp was increased by 5.45% in plants given positive energy. Fruit qualities were also significantly affected by psychoenergy. TSS (Brix) was significantly increased by 13.54% in plants given positive energy as compared to negative energy, and titratable acidity was reduced by 25% due to positive energy. Ascorbic acid was also increased by 30% in plant given positive thoughts. Sun burn was reduced by 54.76% and fruit cracking by 63.64% due to energy of thought. Fruit borer infestation was reduced by 70%, and mite infestation was reduced by 90% in plants given positive energy. The psychoenergetic potential is vast, and its ability to improve crop yield and quality cannot be overstated. The hidden power of thought is being practiced by all, but mostly people do not know this power and use it in an improper manner. This is a high time when we need to practice generating powerful thoughts to change present-day agriculture and its dependents.

Proposed herein is an environment-friendly method to realize oil/water separation. Nylon mesh is exposed to atmospheric pressure plasma for surface modification, by which micro/nano structures and oxygen-containing groups are created on nylon fibers. Consequently, the functionalized mesh possesses superhydrophilicity in air and thus superoleophobicity underwater. The water pre-wetted mesh is then used to separate oil/water mixtures with the separation efficiency above 97.5% for various oil/water mixtures. Results also demonstrate that the functionalized nylon mesh has excellent recyclability and durability in terms of oil/water separation. Additionally, polyurethane sponge slice and polyester fabric are also functionalized and employed to separate oil/water mixtures efficiently, demonstrating the wide suitability of this method. This simple, green and highly efficient method overcomes a nontrivial hurdle for environmentally-safe separation of oil/water mixtures, and offers insights into the design of advanced materials for practical oil/water separation.