Dilla University

This study examined the effectiveness of the Ratio Method (RM) and the Unit Circle Method (UCM) in teaching introductory trigonometry to Ethiopian secondary school students. A quasi-experimental design was employed, involving 82 Grade 10 students assigned to two instructional groups. One group was taught using the Ratio Method, while the other received instruction through the Unit Circle Method. Both groups were taught by the same teacher over a two-week period, using the same curriculum content. Students completed a pre-test, an achievement post-test, and a trigonometric relationships and reasoning post-test after the intervention. Data were analyzed using descriptive statistics and Analysis of Covariance (ANCOVA), with pre-test scores treated as a covariate. The findings showed that students in the Ratio Method group achieved significantly higher scores in both trigonometry achievement and trigonometric relationships and reasoning than those in the Unit Circle Method group after controlling prior knowledge. These differences were statistically significant and were associated with a very large effect for trigonometry achievement and a large effect for trigonometric relationships and reasoning. The findings are interpreted through the lens of Cognitive Load Theory, with attention to the differing cognitive demands associated with the two instructional approaches. The results suggest that ratio-based instruction provides a more accessible foundation for introducing trigonometry, particularly for novice learners and resource-constrained classroom settings. This study highlights the importance of instructional sequencing when introducing trigonometric concepts.

This study evaluated the effects of solar UV-B (Ultraviolet-B) radiation on coffee seedlings at different altitudinal ranges in a tropical environment. A field experiment, conducted using a randomized complete block design, tested four coffee varieties—Fayette, Odisha, Koti, and Hangafa—under natural UV-B radiation and UV-B-blocking sheets at altitudes of 1450, 1850, and 2150 m, with three replications. The results revealed that altitude significantly influenced most growth parameters, except for specific leaf area and primary branch girth. The interaction between altitude and coffee variety affected plant height, primary branch length, and internode length (at p < 0.001, 0.01 and 0.05, respectively), with plant height and primary branch length decreasing as altitude increased. Altitude also impacted leaf area and physiological parameters such as photosynthetic rate (Pn) and transpiration rate. In contrast, the interaction of UV-B and altitude influenced stomatal conductance and intercellular CO2 levels. These findings demonstrate that coffee varieties respond differently to solar UV-B radiation at different altitudes. This highlights the need for location-specific coffee breeding/genetic selection/ in tropical environments to address adaptation to climate change, particularly in relation to increased UV radiation.

The valorization of agro-industrial by-products as functional food ingredients represents a promising strategy for developing sustainable prebiotic sources. This study aimed to formulate and optimize composite flour derived from green banana peel, carrot bagasse, and orange peel, and to evaluate its physicochemical characteristics, inulin recovery, and probiotic growth-promoting as potential prebiotic composite flour. Sixteen formulations were generated using a D-optimal mixture design to assess proximate composition, inulin yield, resistance to simulated gastrointestinal conditions, and stimulation of probiotic bacteria. The composite flours exhibited low moisture (6.70-7.05%), high dietary fiber (12.5-13.25%), moderate protein (7.0-7.6%), and low fat (2.4-2.85%), indicating suitability for functional food applications. Inulin extraction ranged from 12.2% to 19.8%, with the highest yield obtained from a banana-dominant blend. The extracted inulin showed a molecular weight of similar to 6.0 kDa and a degree of polymerization (DP) of 21, consistent with a strong prebiotic profile. Mixture-design optimization predicted that a formulation containing 51.6% banana peel, 20.1% carrot bagasse, and 28.3% orange peel maximizes both inulin yield and probiotic growth. Cultivation with this formulation supported the proliferation of Lactobacillus rhamnosus GR-1 and Bifidobacterium longum BB536, reaching 9.8 x 10(8) CFU mL(-1). Simulated gastrointestinal assays further demonstrated enhanced survival of these probiotic strains in the presence of the composite flour. The results highlight the synergistic contribution of banana-derived fructans and citrus pectic oligosaccharides (POS) in promoting probiotic growth. Overall, this study demonstrates the potential of fruit and vegetable processing residues as sustainable substrates for the development of value-added prebiotic ingredients suitable for functional food formulations.

The majority of agricultural production in countries like Ethiopia depends on rainfall, and climate change primarily affects agricultural activities in such countries. However, different agro-ecological zones had varying degrees of susceptibility. Thus, the objective of this study was to investigate the agro-ecology based vulnerability of smallholder farmers in Gedeo and West Guji zones in Southern Ethiopia. The study measured the vulnerability elements in three agro-ecological zones using the LVI-IPCC vulnerability index. In this study, both primary and secondary data were used. For a household survey, 376 sampled households were randomly selected, and supplemented by focus group discussions and key informant interviews. The results revealed that different agro-ecologies have varying levels of vulnerability to climate change, with lowland agro-ecology being the most at risk due to its low adaptive capacity, high exposure, and sensitivity indices. Due to its higher adaptive capacity index, lower exposure index and moderate sensitivity index, the highland agro-ecology was the least susceptible with an overall vulnerability index of −0.26. Midland agro-ecology was deemed moderately vulnerable. The results highlighted that planned adaptation actions should take local conditions into account and that resilience building strategies are crucial for reducing the vulnerability of smallholder farmers. It is recommended to advocate for stronger policy measures to improve the community’s capacity for adaptation and reduce its exposure to climate change.

This study presents a higher-order uniformly convergent numerical method for a singularly perturbed nonlinear reaction-diffusion equation. The quasilinearization technique is used to transform a nonlinear term into a linear boundary value problem. The equivalent singularly perturbed reaction-diffusion differential equation is discretized using a central finite-difference method on the Shishkin and Bakhvalov meshes. The stability and parameter-uniform convergence are rigorously analyzed and established. Theoretically, the proposed method is of second order. The application of Richardson extrapolation demonstrates that the Bakhvalov mesh achieves a pure CM-4 rate, whereas the Shishkin mesh attains an epsilon-uniform convergence rate of CM-4ln4M. Three numerical examples have been solved to corroborate the theoretical findings.