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.

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.

One crucial metric for estimating a reservoirs and dam’s lifespan is sedimentation. It is dependent upon sediment output, which in turn is dependent upon soil erosion. The study area, the Aguat Wuha Dam, was located in Simada woreda, of northwestern parts of Ethiopia. And the study's goal was to use Arc GIS and RUSLE adjusted to Ethiopian conditions to assess potential soil erosion and sediment output from the watershed and identify hotspot locations for appropriate planning for erosion and sedimentation problem management techniques to make the outputs of the dam project more productive and effective for the proposed and suggested purpose of the dam. To predict the geographical patterns of soil erosion in the watershed, the Geographic Information System (GIS) was combined with the revised universal soil loss equation (RUSLE). A soil erosion map was produced using ArcGIS by utilizing all of the model's parameters, including Erosivity, erodibility, steepness, land use, land cover, and supportive practice factors. The watershed's yearly soil loss varies from 0 to 413.86 tons/ha. In order to determine the erosion hotspot area, the average annual soil loss value was discovered to be 9.24 tons/ha/year and was categorized into six erosion severity classes: low, moderate, high, very high, severe, and very severe. These findings indicated that 162.57 ha and 699.17 ha of the watershed were considered to be extremely and severely vulnerable to soil erosion, respectively. It was discovered that the anticipated sediment yield supplied to the outlet varied from 0 to 104.94 tons/ha/year. By standing from the implications of the assessments of the geological, geotechnical, topographical, and socioenvironmental considerations Watershed management is the most effective way to reduce the amount of sediment produced and the amount that enters the reservoir among the several reservoir sedimentation control options that are available.

Heat transfer fluids (HTFs) are critical in numerous industrial processes, enabling efficient heat exchange and precise temperature control. HTF degradation, primarily from thermal cracking and oxidation, negatively impacts system performance, reducing fluid lifespan and increasing operational costs, thus necessitating regular monitoring and proactive management. This review assesses optimal sampling frequencies for organic and synthetic HTFs, considering degradation mechanisms, relevant analytical parameters, and the economic advantages of proactive monitoring. The objective of this review is to examine HTF degradation mechanisms, compare organic and synthetic fluid properties and their impact on sampling frequency, and discuss strategies for optimising system performance and extending fluid life through effective HTF condition management. The article highlights the importance of fluid management, including appropriate fluid selection, to optimise system and fluid health, which is crucial for maximising their lifespans, ensuring safe operation, and minimising costs.

Work is reported on thermal-induced redshifts of quantum particle plasmon. The redshifts are predicted to be caused indirectly by the quantum size effects. The particles are enlarged when temperature increases, and consequently, quantum size effects modify the plasmon but not the band structure. It has been modeled for metallic quantum particles. The results are also instructive to other quantum systems, such as complex molecules. Every electron inside the quantum particle is taken into account. Tiny quantum size effects are harvested, and the redshift becomes significant. Experimental evidence is also given for the spectral redshift. Faujasite zeolites were synthesized. Optical spectroscopy has been carried out, and the resulting spectra showed a significant redshift with the increase in temperature.