Chuka University

<title>Abstract</title> This paper investigates the impacts of varying zonal harmonics up to J4 on dynamics of a satellite around out-of-plane equilibrium points of the restricted three-body problem with variable masses. The motion and mass variations of the primaries are described by the Gylden-Mestschersky problem (GMP) and the unified Mestschersky law (UML), respectively.The non-autonomous differential dynamical equations of the satellite are obtained and transformed to an autonomized system, with the help of the Mestschersky transformation, the UML, the particular integral and solutions of the GMP. Four out-of-plane equilibrium points (OEPs) denoted by and are obtained. Further, the OEPs are seen to be unstable and a numerical application is rendered for a satellite placed in the neighborhood of PQ Pegasi. It is observed that Increasing values of zonal harmonics results in the satellites position at the OEPs drifting towards the binary while the satellite is forced away from the PQ Pegasi at the points. A contrary observation occurs when the mass variation is large. Also, the zero velocity curves (ZVCs) are explored and it is seen that increasing the mass variation parameter increases the forbidden region in the presence or absence of zonal harmonic terms. Also, it is seen that, the zonal harmonic J4 term increases the region where motion is permissible, while the J2 term decreases it. Furthermore, it was seen that the orbits of the satellite around the OEPs could be quasi-periodic, divergent straight line or a chaotic. The study is applicable in space missions and astronomy.

Achievement in Mathematics at Kenya Certificate of Secondary Education (KCSE) examinations has been poor over the years. The low achievement has partly been blamed on teaching methods which do not actively involve learners in the learning process, depriving them of taking charge of their learning. The aim of this study was to investigate the effectiveness of cooperative learning strategy in enhancing students’ attitude in Mathematics in secondary schools in Meru South Sub- County. The study employed the Solomon Four-Group, Non-equivalent Control Group Design. The target population for the study was 2430 form three students in 44 co-educational secondary schools in Meru South Sub-County. The sample comprised 164 form three students from four co-educational schools within the Sub-County. Random sampling was used to select the four schools from a list of prequalified schools. Prequalification was based on the number of students, students’ entry behaviour, availability of teaching/learning resources and teachers' qualification. Simple random sampling technique was used to assign participating schools to experimental and control groups. A Mathematics Achievement Test (MAT). The instruments were piloted in Maara Sub-County in a co-educational secondary school with similar characteristics as the sampled schools. The reliability of the research instruments was estimated using Cronbach’s Alpha. A reliability coefficient of 0.79 for MAT was obtained. Validity of the instruments was ensured through expert judgment. Data was analyzed using both descriptive and inferential statistics. The study found that MAT mean score for male (3.21) was lower than that of female (4.52). further, the t-test analysis established that the difference was no statistically significant between the mean scores for female and male students at α=0.05 significance level (t (86)=11.87, p&gt;0.05).

Statistical software packages are essential tools in undergraduate education, particularly in the Fourth Industrial Revolution, enabling students to perform complex data analyses and gain practical experience in statistical methods. The integration of these tools into the curricula enhances students’ analytical skills and prepares them for data-driven decision-making in various fields. This study investigates the utilization of statistical packages by undergraduates of Mathematics Education at a university in West Africa. The study aims to determine the level of use of statistical packages among students, identify the challenges faced, and propose strategies to overcome these challenges. A descriptive survey design was used, with data collected from 150 students using structured questionnaires. The data were analysed using descriptive statistics of mean and standard deviation. The results indicate that the students showed moderate use of statistical packages, with a cluster mean of 2.88 (SD = 1.09). With respect to the challenges faced in the utilization of statistical packages, the primary barriers included limited access to computers and the internet (mean = 2.97), high software costs (mean = 2.93), and insufficient training opportunities (mean = 2.99). Based on the findings, the study concluded that while students are aware of statistical packages, their usage remains moderate, hindered by infrastructural and training deficiencies. Strategies such as integrating software training into the curriculum and providing access to free or open-source tools are recommended. Integrating these tools into curricula in the present era of the Fourth Industrial Revolution, supported by appropriate resources and training, is essential to foster a comprehensive understanding of statistical methods and their applications.

This paper examines the linguistic features employed by political leaders in development discourse in Kimeru FM radio stations in Kenya. It specifically focuses on how language is used to frame issues of sustainable development. Guided by Norman Fairclough’s Critical Discourse Analysis theory, the study adopted a qualitative research design, particularly a focused descriptive approach. Data were drawn from twenty purposively sampled talk shows and interviews on Muuga FM and Meru FM, covering the period between 2020 and 2024. The programs were downloaded from online platforms, transcribed, and analysed using a lexical–grammatical checklist. The findings revealed that political leaders used distinct linguistic features, including nominalisation, passivisation, transitivity, modality, and ideological framing, to construct and advance development narratives. These linguistic choices enabled the leaders to control the representation of development processes, manage responsibility, and reinforce their authority in public discourse. The study concludes that linguistic strategies are central in shaping how development is perceived and communicated in Kimeru FM radio stations.

There exists limited green gram production in Kirinyaga County. Increasing green gram production and yield in this area can make it a substitute of beans, cowpeas and maize. Farmers in this area have limited information on use of rhizobia and phosphorus and using the right spacing hence resulting to low yields. This study aimed at evaluating the effect of rhizobia inoculation, phosphorus application and planting density on yield and net economic analysis of green gram production. The study was conducted at Kenya Agricultural and Livestock Research Organization (KALRO), Industrial Crops Research Centre – Mwea where the experiment was laid out as a 3 x 3 x 3 factorial arrangement using Randomised Complete Block Design and replicated three times and in two consecutive cultivations. Treatments included three levels of phosphorus (0 kg/ha, 60 kg/ha and 90 kg/ha), three planting densities (40 x 10 cm, 45 x 15 cm, and 50 x 20 cm) and three levels of rhizobium inoculation (0 g, 20 g and 40 g per kg of seeds) in K26 variety of green gram. Data was collected on number of pods and grains per pod, grain yield and net economic benefit. Data collected was subjected to analysis of variance using Statistical Analysis Software (SAS) and significantly different means separated using the Turkeys test at α = 0.05. The findings indicated that rhizobia and phosphorus application and plant density had a significant effect on the grain yield and net economic benefit. There was significant (p &lt; 0.05) interaction effect for rhizobia inoculation, phosphorus application and planting density on the grain yield per green gram plant. The yield increased from 98.81 kg and 212.29 kg; 64.15 kg and 118.52 kg in trial I and II, respectively. The analysis of integrated treatment effect of rhizobia rates, phosphorus application and densities showed that the net economic benefit ranged from KSh -21205 to KSh 24512 .5 and KSh -600 to Ksh -24600 for trial I and II, respectively. Treatment with the highest net economic benefit was rhizobia 40 g, phosphorus 20 kg/Ha and 45 x 15 cm. Application of rhizobia rate 40g/Ha, phosphorus 60 kg/Ha and at planting density of 45 × 15 cm produced the highest grain yield. The study recommends application of rhizobia at 40 g/Ha, phosphorus at 60 kg/Ha and planting density at 45 x 15 cm to produce the highest grain yield and rhizobia 40 g, phosphorus 20 kg/Ha and 45 x 15 cm for highest net economic benefit.

Consumption-based food resilience strategies (CBFRS) are commonly employed by households in semi-arid regions to cope with recurrent food shortages. This paper examines the adoption and influence of CBFRS on livelihood outcomes in Makueni County, Kenya. A sample size of 399 rural households was drawn from three sub-counties (Mbooni, Makueni and Kibwezi West) through multistage sampling, comprising stratified, purposive and simple random sampling techniques. The study adopted a descriptive survey research design to meet the research objective. Data was collected through structured questionnaires, key informant interviews and direct observations and analyzed using descriptive and regression analysis. Results showed that households employed variable consumption-oriented strategies to manage food availability and access during times of stress or scarcity. CBFRS such as meal reduction, food substitution, rationing and preservation were practiced, particularly during droughts. The study findings revealed a moderate adoption of CBFRS (M = 3.011) in Makueni County The regression results revealed a statistically significant negative association between the adoption of consumption-based FRS and overall livelihood outcomes (b = -0.269, p &lt; 0.001)), suggesting that CBFRS are largely coping mechanisms rather than proactive resilience measures. While CBFRS provide temporary relief, they compromise nutrition and long-term well-being. Constraints such as water scarcity, financial limitations, and lack of awareness further hinder effective CBFRS adoption are CBFRS are not productive but coping mechanisms amidst food stress; hence, they can erode food system resilience The paper recommends targeted interventions to reduce reliance on CBFRS by enhancing institutional and farm-based strategies.

Class struggle has been a pertinent issue in Literature. Literary texts have always presented conflicts between the oppressed and the oppressor. These conflicts emerge as the oppressed group try to free themselves from the yoke of oppression. While the struggle for a better society used to be carried out by men because they were believed to be brave and strong, women joined them. When this occurred, they work as a united team to complement each other in liberating the society. Therefore, the aim of this study is to examine how solidarity of men and women triggers class struggle in Ngugi’s Petals of Blood and Sembene’s God’s Bits of Wood. The texts under study were selected because their thematic content is largely based on class struggle. The analysis was done using Marxism theory which urges the oppressed group to rise and unite so that they can demand for what belongs to them. This tenet was employed in the study to examine how men and women have not only risen but also united to complement each other in the struggle. The study went further to examine the changes that occur in the novels under study when men and women work together to demand for better working conditions and developments. The researcher used qualitative approach in data analysis because the data from the texts under study was non-numerical. The study is significant because it provides an insight on how the unity of men and women can trigger class struggle.

Pollution from anthropogenic and natural processes threatens most fresh water resources. In Kenya, drought and occasional floods affects water quality negatively impacting health of humans and ecosystem. Currently the use of in situ observation methods for monitoring water quality is inadequate, periodic and at selected sample points. The potential of remote sensing-based techniques in examining water quality in open water bodies is explored. Aim of this study was to assess variability in Chlorophyll concentration (Chl_a), water temperature (SST) and Suspended Sediment Concentrations (SSC) of Ndakaini Dam before and after the destructive April-May 2018 floods. Landsat 8 OLI imagery and QGIS V 2.14 Essen geospatial software were used. The results indicated that Chlorophyll concentration levels decreased by 0.26mg/l, water temperature dropped by 30C while Suspended Sediment increased by 2.57mg/l. Generally, analysed water quality parameters showed a spatial and temporal variation across the April-May 2018 floods. Ndakaini dam was found to be a low-level pollution mesotrophic reservoir.