FACULTY OF PHYSICAL SCIENCES

A geoelectrical imaging survey was conducted at Uwelu and its environs in Egor Local Government Area of Edo State, Nigeria, for Shallow site investigation in order to determine the applicability of 2-D resistivity imaging in studying the subsurface, which in turn determines how feasible the area would be in terms of erection of structures that will stand the test of time. The area is underlain mainly with low resistivity materials with minor intrusion high resistivity materials like gravel, limestone basalt and slate. Geophysical survey was carried out using 2-D electrical resistivity imaging technique. The Wenner Alpha configuration was employed. Field data were obtained for ten electrical imaging lines, at Uwelu market area in Egor Local Government Area, subjected to inversion, in order to remove geometrical effects from the pseudo-section and produce an image of true depth and true formation resistivity. The 2-D electrical investigation at the survey site showed that the soil lithology compartment will be a good site for big building and other construction works even for shallow site works.

This study develops a machine learning model to predict abnormalities in commercial airplanes using real-world Automatic Dependent Surveillance-Broadcast (ADS-B) data, focusing on altitude changes exceeding 100 feet in 10 seconds. Following the methodology established by Passarella et al. (2024), this research implements and compares 25 different machine learning algorithms, ultimately selecting Quadratic Discriminant Analysis (QDA) as the optimal approach. The dataset comprises 167,844 records, including 84,074 normal and 83,770 abnormal instances, with features such as altitude, velocity, heading, latitude, and longitude. The theoretical foundation covers the comprehensive taxonomy of machine learning methods, from supervised learning algorithms like Support Vector Machines and Decision Trees to unsupervised approaches such as K-Means clustering. The QDA model achieves superior performance with 93-97% accuracy, 0.96-0.97 ROC-AUC, validated through stratified 5-fold cross-validation. Visualizations, including altitude plots and ROC curves, enhance interpretability for aviation professionals. This research demonstrates that QDA's ability to model non-linear decision boundaries with class-specific covariance matrices makes it particularly suitable for complex aviation data patterns, supporting enhanced flight safety and operational efficiency.

The increasing demand for secure, transparent, and efficient electoral processes has led to the adoption of online voting systems in universities. This project presents a PHP-based online voting system designed to provide a secure, user-friendly, and tamper-proof election platform for universities. The system enables student authentication, candidate registration, real-time vote
tallying, and automatic result generation after a set period. Security measures such as one-time voting enforcement and database encryption ensure election integrity. By leveraging web technologies, this system enhances electoral accessibility while minimizing fraud and administrative overhead, offering a scalable solution for university elections.

Linear programming is one of the most effective techniques used in decision-making and optimization problems, especially in business and industrial applications. This project focuses on the use of a linear programming to determine the most efficient way of maximizing profit and minimizing cost. Mouka Foam Company, Benin City, was used as a case study to demonstrate how mathematical models can support better production and resource allocation decisions The simplex method was applied to the formulated linear programming problem derived from the assumed but realistic data of Mouka Foam Company. The process involved defining the objective function, identifying the constraints, introducing slack variables, and systematically applying the simplex algorithm to reach an optimal solution. The entire computation was manually solved and verified to ensure the accuracy of results The result of the analysis shows that the simplex method provided an optimal solution that maximizes profit while minimizing production cost under the given constraints. The findings prove that linear programming is a reliable and efficient mathematical tool for managerial decision-making, especially in production planning and cost optimization.

Access to academic materials is one of the main key factors that can affect the academic performance of a student. The traditional method of accessing materials such as handwritten lecture notes, printed handouts, and textbooks are still useful but all have their own challenges in trying to use them. These challenges can lead to loss of material and accessibility. This project highlights the need for a digital and centralized approach to academic resource management. The proposed system in this work is the Student Academic Resource Hub (SARH) which is designed to serve as a digital repository for students and lecturers where
they can upload, access, and download academic materials such as lecture notes, past questions and other study resources according to their academic levels or courses. The design of the Student Academic Resource Hub is focused on creating a simple user friendly web platform that uploading and accessing materials easy for students and lecturers. The SARH was built with the frontend and the backend. The database is used for storing users’ data and uploaded resources. Certain implementation libraries were integrated to handle secure authentication and data protection. The result of this project is a developed system which is capable of providing an efficient, secure, and scalable alternative to the manual methods currently in use.

The MERN ChatApplication for College Students is a contemporary web-based communication tool created to facilitate seamless interaction and collaboration among college students. In today's digital era, effective communication plays a crucial role in improving learning outcomes and building a sense of community among students. Current chat applications often lack the specific features and security measures required for the unique needs of college students. Taking into consideration the constraints and the scope of the project, which is the University of Benin, Department of Computer Science, the method proposed by this project is a MERN Chat Application which aim to tackle these challenges by offering a secure, user friendly, and feature-rich platform tailored to the needs of college students. By utilizing the MERN stack (MongoDB, Express.js, React.js, Node.js), the application provides a strong and scalable solution for real-time messaging, group discussions, and academic collaboration. Key features of the MERN Chat Application include secure user authentication, dedicated group chat spaces, real-time messaging capabilities, and compatibility across various devices and web browsers. The application places a high priority on user privacy and data security, ensuring that student information remains confidential and always protected. Through a combination of cutting-edge technology, user-friendly design, and comprehensive features, the MERN Chat Application aims to transform the way college students communicate and collaborate. By offering a centralized platform for academic discussions, resource sharing, and group projects, the application aims to improve learning outcomes, encourage community engagement, and promote collaborative learning among college students.

This study explores the methodology underlying the pricing of call options using continuous-time models. Beginning with the Wiener process as a foundational model, the research extends into stochastic calculus and the derivation of the Black-Scholes equation. The analysis delves into the fundamental properties of Brownian motion, the normal distribution, and stochastic differential equations to establish a rigorous mathematical framework for asset price movements.

A key focus is placed on the arbitrage argument, which ensures that financial markets remain free from riskless profit opportunities. The no-arbitrage condition is then used to derive the Black-Scholes partial differential equation, which governs the pricing of options. Through a series of transformations, the equation is reduced to the heat equation, allowing for an analytical solution to be obtained. Finally, the study applies this methodology to derive explicit pricing formulas for European call and put options, highlighting the impact of volatility, risk-free interest rates, and time to maturity on option values. By formalizing the theoretical framework with stochastic calculus and arbitrage pricing theory, this research provides a robust foundation for the application of call option models in financial engineering.

Nosocomial infections, also known as hospital-acquired infections, are bacterial infections contracted within healthcare settings. They contribute significantly to the burden of disease by prolonging hospital stays, increasing treatment costs, complicating surgical outcomes, and, in severe cases, leading to death. Methicillin resistant staphylococcus aureus (MRSA) is the most isolated
pathogen of nosocomial infections and the most studied in the literature. Despite their impact, awareness of nosocomial infections remains limited, leaving patients, healthcare workers, visitors, and even family caregivers vulnerable to its transmission. In low-income and middle-income countries the practice of a family caregiver assisting an inpatient is common, and they can contact and transmit infections while carrying out various activities within the hospital environment. Deterministic and stochastic models have been widely applied to understand the transmission dynamics of nosocomial infections and provide valuable insights. However, existing models have often overlooked the role of patients’ family caregivers, who can act as important but underrecognized vectors of transmission. In this thesis, deterministic and stochastic models that explicitly incorporate family caregivers as a distinct transmission pathway of methicillin-resistant Staphylococcus aureus (MRSA) are developed. For the deterministic framework, the basic reproduction number �0 is derived along with the conditions for disease-free and endemic equilibria. The stochastic framework developed using a Continuous-time Markov Chain (CTMC) extends the deterministic model by incorporating random fluctuations through its drift and diffusion terms. This provides deeper insight into the system’s variability, extinction probabilities, and outbreak risks that cannot be fully captured by the deterministic model. For the deterministic model, the basic reproduction number is evaluated and subjected to sensitivity analysis, using plausible parameter values from surveillance studies within Nigerian hospitals, whereby revealing the dominant influence of hand-hygiene compliance of caregivers and healthcare workers, as well as decontamination rates of both caregivers and healthcare workers. The stochastic simulation in MATLAB gives the stochastic sample paths, time-series behaviours of the state variables and extinction probability. The numerical results illustrate that while the deterministic model captures mean epidemic behaviours, stochastic models reveal substantial variability and probability of infection extinction especially in settings with effective hand hygiene compliance of caregivers and healthcare workers. These analyses reveal the importance of integrating patients’ family caregivers in modeling the spread of MRSA in hospitals.

The exponential distribution became the cornerstone of survival analysis and reliability engineering throughout the latter half of the 20th century and it is imperative to mention that the Successive times in exponential distribution are assumed to occur independently and randomly over time with a constant rate. The aim of the study was to develop a generalized and flexible bivariate exponential distribution that will incorporate correlation parameter 𝜌, extending the domain to a positive real-line using the framework of linear regression. A secondary dataset from Federal Road Safety Corps on road accidents in Imo State from 2020 to
2024 was used in the study and it was obtained from the Head office of Federal Road Safety Corps, off Egbu road Owerri, Imo state. In the study, we developed a generalized and bivariate exponential model that incorporates a correlation parameter, while preserving analytical simplicity. The proposed model, referred to as the New Correlated Bivariate Exponential Distribution (NCBED). The consistency of the NCBED was assessed using Kolmogorov Smirnov and Cramer Von Mises tests, in comparison with the baseline Grine model (2018). The Federal Road Safety (FRSC) dataset demonstrates that both injury and fatality data follow heavy-tailed exponential-type distributions and the NCBED provided a superior fit compared to the baseline model, capturing real-world correlations between crash outcomes. The findings indicate that the Maximum Likelihood estimates of the proposed model are consistent with the nature of the model.

This study examines how sentiment analysis shapes brand reputation management in a digital environment dominated by user-generated content and real-time public feedback. Using a mixed methods approach, the research integrates quantitative sentiment mining—via VADER and TextBlob—with qualitative interviews from brand managers and sentiment analysis experts. Quantitative data from social media and review platforms were analyzed to determine sentiment polarity and trends, while qualitative insights clarified how organizations interpret and apply these results. Findings show that sentiment analysis enhances reputation management by enabling real-time monitoring, early detection of emerging crises, and data-driven strategic decisions. Positive sentiment corresponds withstronger brand equity and loyalty, whereas negative sentiment, particularly on high-velocity platforms like Twitter, accelerates reputational risk. The study concludes that sentiment analysis is essential for proactive brand management and recommends broader adoption of AI-driven tools, improved crisis protocols, and continuous model updates to address linguistic nuances and reduce algorithmic bias.