FACULTY OF PHYSICAL SCIENCE

Five (05) granitic rock samples from Igarra-Ugbogbo area in Akoko-Edo Local Government Area of Southwestern Nigeria were obtained with the aim of determining their geochemical and mineralogical properties using XRF, XRD techniques. Results of the analysis revealed the presence of SiO2 (62.05-79.63wt.%), Al2O3 (10.88-15.10wt.%), Fe2O3(T)* (0.37- 6.29wt.%), K2O (0.89- 8.248wt.%), Na2O (0.17-10.02wt.%) and CaO (0.32-4.68wt.%). The abundance of these major oxides in the samples showed that samples OGB01 and GB05 are felsic magma while UNE02 is probably from a pegmatitic magma and EFU03 and GBO04 are most likely formed from an intermediate magma. Using Al2O3 classification scheme, its showed that OGB01 and UNE02 are peraluminous while EFU03, GBO04, OGB05 are peralkaline. The XRD analysis revealed the presence of quartz, alkali eldspars (microcline, orthoclase and sanidine), plagioclase feldspars (albite and anorthite), muscovite, lime, geothite. The modal composition of the quartz, alkali feldspar, plagioclase were plotted on a QAP diagram which showed that the rock falls within the granite and Quartz-rich granitiod.

Second-order partial differential equations (PDEs) are fundamental in mathematical physics, engineering, and applied sciences. These equations involve second-order derivatives of an unknown function with respect to multiple independent variables. They are broadly classified into three types: elliptic, parabolic, and hyperbolic, based on their characteristic behaviour. Notable examples include the Laplace equation, the heat equation, and the wave equation, each governing essential physical phenomena such as steady-state distributions, diffusion processes, and wave propagation, respectively. Solutions to second-order PDEs often require analytical or numerical techniques, including separation of variables, Green’s functions, Fourier and Laplace transforms, and finite difference methods. Boundary and initial conditions play a crucial role in determining well-posed solutions. Recent advancements in computational methods, such as finite element analysis and deep learning-based PDE solvers, have significantly improved the ability to model complex systems.

In kernel density estimation, the choice of kernel plays a crucial role in accurately estimating the underlying probability density function. This project focuses on comparing three commonly used kernels: Gaussian, Epanechnikov, and Biweight. The objective is to plot a graph that visually demonstrates the differences between these kernels and evaluate their efficiency using the mean square error metric. First, the theoretical foundations of kernel density estimation are explored, emphasizing the importance of choosing an appropriate kernel. The Gaussian kernel, known for its smoothness and symmetry, is widely used due to its desirable properties. The Epanechnikov kernel, with its compact support and optimal bias-variance trade-off, is another popular choice. Lastly, the Biweight kernel, which balances robustness and efficiency, is considered. To compare these kernels, a graph is plotted to visualize their shapes and characteristics. This graphical representation allows for a clear understanding of how each kernel affects the density estimation. Additionally, the mean square error metric is employed to quantitatively assess the efficiency of each kernel. By calculating the squared differences between the estimated density and the true density, the mean square error provides a measure of accuracy. Through this analysis, valuable insights into the strengths and weaknesses of each kernel can be gained. The graph and mean square error comparisons reveal how the choice of kernel impacts the estimated density function. This information can guide researchers and practitioners in selecting the most suitable kernel for their specific applications. Overall, this project contributes to a deeper understanding of the choice of kernel in kernel density estimation. By focusing on the Gaussian, Epanechnikov, and Biweight kernels, both their graphical representations and efficiency evaluations shed light on their performance in estimating probability density functions.

This study focuses on the design and implementation of a Computerized Crime Reporting and Management System aimed at addressing the inefficiencies associated with manual crime reporting methods. The system provides a digital platform where crimes can be reported, tracked, and managed efficiently. Key functionalities include online report submission, automated case assignment, status tracking, and centralized database storage for crime data. The system also supports real-time communication between citizens and law enforcement agencies, enabling improved responsiveness and transparency. Through the use of secure login mechanisms, role-based access control, and data encryption, the system ensures the confidentiality and integrity of sensitive crime-related information. The implementation process involved system modeling, software development, database integration, and rigorous testing for performance, functionality, and security. Testing confirmed the system’s ability to handle user inputs, protect data, and operate under real-time constraints. The computerized system enhances accessibility, reduces delays in reporting, and allows for effective data analysis, making it a valuable tool for law enforcement agencies. This study demonstrates that digital crime management systems can significantly improve the accuracy, speed, and reliability of crime data handling, ultimately contributing to a more efficient and accountable criminal justice process.

Linearized water wave theory is a fundamental concept in fluid dynamics that has been extensively used to study wave propagation in various aquatic environments. Water waves play a crucial role in many engineering and scientific applications, including ocean and coastal engineering, ship hydrodynamics, and offshore engineering. However, the complexity of nonlinear wave dynamics has limited the accuracy of traditional numerical models, emphasizing the need for a simplified yet robust approach. Linearized water wave theory offers a promising solution by assuming small-amplitude waves, enabling the simplification of the governing equations and providing an efficient tool for wave analysis. This project explores the mathematical and physical principles underlying linearized water wave theory and its application in various fields such as oceanography, coastal engineering and naval architecture. The study begins with an overview of the basic equations governing water wave motion including the linearized Euler equation and boundary conditions. The dispersion equation which relates the wave frequency to its wavenumber is derived and analysed to properly understand wave propagation characteristics. In this study, we developed and applied linearized water wave theory to investigate wave propagation in a simplified fluid domain. We also discretized the linearized Navier-Stokes equations and then introduced a wave-like solution to represent the small-amplitude waves. By substituting this solution into the linearized equations, we obtained a set of ordinary differential equations that describe the wave propagation characteristics. Through mathematical analysis and numerical simulations, this study aims to provide a comprehensive understanding of linearized water wave theory and its applications in fluid dynamics. The applications of this study are diverse and far-reaching. Our results can be used to improve the design and optimization of various aquatic structures, such as seawalls, breakwaters, and offshore platforms, by providing a better understanding of wave-structure interactions. Additionally, our findings can be applied to enhance the accuracy of wave forecasting models, which are crucial for coastal erosion prediction, ship navigation, and offshore operations. Furthermore, the linearized water wave theory can be extended to study more complex wave phenomena, such as wave-current interactions and wave-induced sediment transport, offering a promising avenue for future research.

Antibiotics resistance is an emerging problem worldwide which can develop as a result of antibiotics misuse by humans or overuse in animal feeding and treatment. This study was aimed at investigating the prevalence of Escherichia coli and Salmonella spp. and study the antibiotic resistance pattern of isolates. a total of 40 samples were collected from four different markets namely; Okha, Santana, Oba and Ekiosa markets in Benin City and were analysed using standard microbiological methods for the investigation. Results from the investigation showed that E. coli and Salmonella spp were present in almost all of the samples. The Total Aerobic Count showed that Santana market (5.97±0.53 cfu/g) had the highest average count whereas the lowest average count was observed in Ekiosa market
(4.29±0.49cfu/g). The total E. coli count on Eosin-Methylene Blue Agar showed that the highest E. coli count was observed in samples taken from Ekiosa market (1.93±0.38 cfu/g), whereas, the lowest was observed in samples collected from Oba market (1.69±0.40 cfu/g). The Total Salmonella count on Salmonella-Shigella Agar showed that Oba market (2.502±0.32 cfu/g) had the highest count while Ekiosa market (1.073±0.22 cfu/g) had the lowest count. Based on the number of samples collected from each market the prevalence rate shows that E. coli was isolated from 25% of the samples collected while Salmonella was isolated from 45% of the samples collected. The antibiotics resistance pattern showed that all E. coli isolates were resistant to cefixime, augumentin, nitrofurantion and cefuroxime, while all Salmonella isolates were resistant to cefixime, augumentin, ceftazidime and cefuroxime. Monitoring of antimicrobial resistance in E. coli and Salmonella spp. isolates is valuable for epidemiological uses and for monitoring the increase of antimicrobial resistance among different microbial species.

The study was designed to assess the concentrations of zinc and chromium in some commercially available green and Black sold teas they include Lipton, Top tea, Richmond tea, Cinnamon Tea and Natural green tea within Benin City, Nigeria. Five of the most popular brands among consumers were purchased in the open market. They were digested, infused (cold and hot) and analyzed for their heavy metal content using the atomic absorption spectrophotometer. The heavy metal concentration varied among the different brands of tea in the study. In the tea samples zinc concentration ranged between 35mg/ kg to 70mg/kg while chromium gave the lowest value of 0.65mg/kg and maximum concentration of 22mg/kg. The cold and hot infusion samples revealed very low concentrations of both zinc and chromium (most of them below detectable limits) ranging between 0.03 mg/l to 0.10 mg/l. In conclusion, the risk of heavy metal exposure via the consumption of these tea is low, with no significant health implications to onsumers and thus does not pose a threat to food safety

Linearized water wave theory is a fundamental concept in fluid dynamics that has been extensively used to study wave propagation in various aquatic environments. Water waves play a crucial role in many engineering and scientific applications, including ocean and coastal engineering, ship hydrodynamics, and offshore engineering. However, the complexity of nonlinear wave dynamics has limited the accuracy of traditional numerical models, emphasizing the need for a simplified yet robust approach. Linearized water wave theory offers a promising solution by assuming small-amplitude waves, enabling the simplification of the governing equations and providing an efficient tool for wave analysis. This project explores the mathematical and physical principles underlying linearized water wave theory and its application in various fields such as oceanography, coastal engineering and naval architecture. The study begins with an overview of the basic equations governing water wave motion including the linearized Euler equation and boundary conditions. The dispersion equation which relates the wave frequency to its wavenumber is derived and analysed to properly understand wave propagation characteristics. In this study, we developed and applied linearized water wave theory to investigate wave propagation in a simplified fluid domain. We also discretized the linearized Navier-Stokes equations and then introduced a wave-like solution to represent the small-amplitude waves. By substituting this solution into the linearized equations, we obtained a set of ordinary differential equations that describe the wave propagation characteristics. Through mathematical analysis and numerical simulations, this study aims to provide a comprehensive understanding of linearized water wave theory and its applications in fluid dynamics. The applications of this study are diverse and far-reaching. Our results can be used to improve the design and optimization of various aquatic structures, such as seawalls, breakwaters, and offshore platforms, by providing a better understanding of wave-structure interactions. Additionally, our findings can be applied to enhance the accuracy of wave forecasting models, which are crucial for coastal erosion prediction, ship navigation, and offshore operations. Furthermore, the linearized water wave theory can be extended to study more complex wave phenomena, such as wave-current interactions and wave-induced sediment transport, offering a promising avenue for future research.

Radon is an odourless, invisible, radioactive gas naturally released from rocks, soils and water. Radon can get into homes and buildings through small cracks or holes and build up in the air. Over time, breathing in high levels of radon can cause lung cancer. Radon-222 is a naturally occurring radioactive gas that accounts for approximately half of the human annual background radiation exposure globally. Chronic exposure to radon and its decay products is estimated to be the second leading cause of lung cancer behind smoking (WHO, 2009; UNSCEAR 2000). Ionizing radiation emitted as a result of much energy from radon and its progeny can induce variety of cytogenetic effects that can be biologically damaging and results in an increased risk of carcinogenesis (The process in which normal cell are transformed into cancer cell). Suggested effects of alpha particle emission from Radon include mutation, chromosome aberrations, generation of reactive oxygen species, modification of cell cycle, up or down regulation of cytokines and the increased production of proteins associated with cell- cycle regulation and the transformation of normal cell into cancer cells. The Environmental Protection Agency recommends 148 Bq/m3 as the action level. On the other hand, International Commission for Radiation Protection (ICRP) recommends 200 Bq/m3 as the action level, while WHO recommended 100Bq/m3 as action level. The main objective of this study is focuse on how radon is established as a health hazard, its effects on cellular metabolism and energy production, and the potential of radon as a therapeutic agent for metabolism disorder, way of radon detection and measurements, methods of reducing and controlling high indoor radon concentration, and what are the recommended international action levels of radon concentrations. It mainly focuses on the health perspective of radon studies because it is a crucial and hot issue in the world today. In most developing countries like Nigeria, radon studies are not well investigated and the high mortality rate of lung cancer is of the increase.

This project investigates improving pathfinding algorithms in Geographic Information Systems (GIS) by optimizing the calculation of geodesics. Geodesics refer to the shortest paths along the curved surface of the Earth, as opposed to straight lines drawn on a flat map. This is crucial for accurate navigation, especially over long distances. Traditional GIS pathfinding algorithms often rely on simpler Euclidean distance calculations, which can lead to significant errors.The objective of this study is to develop or improve upon existing methods for finding optimal geodesics paths within a GIS environment. This will enable more accurate and efficient navigation for various applications, such as: route planning for vehicles, pedestrians, and drones, search and rescue operations, ecological studies analyzing animal movement patterns. The study will explore different algorithms for calculating geodesics on a geoid (Earth's mathematical representation). This could involve techniques like Dijkstra's algorithm adapted for curved surfaces or A* search with appropriate heuristics for geodesic distances. The study might explore methods to optimize the pathfinding process. This could involve strategies like pre-computing geodesics for frequently used routes or implementing techniques to reduce computational complexity. This study by optimizing geodesics paths for navigation has the potential to significantly enhance the capabilities of GIS for various applications requiring accurate and efficientpathfinding.