A new method has been proposed to estimate top heat losses of vertical flat plate liquid/air collectors with double glazing. Empirical relations have been developed for the temperatures of glass covers, thus facilitating the calculation of individual heat transfer coefficients. The values of individual heat transfer coefficients therefore obtained can be used in the proposed analytical equation for the estimation of the top heat loss coefficient of the vertical collector with double glazing. The analytical equation has been developed for collector tilt angle of 60 to 90 degrees, plate temperature of 323 K to 423 K, absorber coating emittance of 0.1 to 0.95, air gap spacing of 20 mm to 50mm between the plate and inner glass cover, air gap spacing of 20 mm to 50mm between glass covers, wind heat transfer coefficient of 5 W/m2K to 30 W/m2K, and ambient temperature of 263K to 313K. The accuracy of the analytical equation has been validated for the said range of variables in comparison to numerical solutions, and the values of the top heat loss coefficient are found to be within 2.5 percent compared to numerical solutions.

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.

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 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.

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.