International Journal of Mathematical Sciences and Computing @ijmsc
Journal articles - International Journal of Mathematical Sciences and Computing
All articles: 294
Scientific article
Many different methods are applied and used in an attempt to solve higher order nonlinear boundary value problems (BVPs). Galerkin weighted residual method (GWRM) are widely used to solve BVPs. The main aim of this paper is to find the approximate solutions of fifth, seventh and ninth order nonlinear boundary value problems using GWRM. A trial function namely, Bezier Polynomials is assumed which is made to satisfy the given essential boundary conditions. Investigate the effectiveness of the current method; some numerical examples were considered. The results are depicted both graphically and numerically. The numerical solutions are in good agreement with the exact result and get a higher accuracy in the solutions. The present method is quit efficient and yields better results when compared with the existing methods. All problems are performed using the software MATLAB R2017a.
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Construction of Fractals based on Catalan Solids
Scientific article
The deterministic fractals play an important role in computer graphics and mathematical sciences. The understanding of construction of such fractals, especially an ability of fractals construction from various types of polytopes is of crucial importance in several problems related both to the pure mathematical issues as well as some issues of theoretical physics. In the present paper the possibility of construction of fractals based on the Catalan solids is presented and discussed. The method and algorithm of construction of polyhedral strictly deterministic fractals is presented. It is shown that the fractals can be constructed only from a limited number of the Catalan solids due to the specific geometric properties of these solids. The contraction ratios and fractal dimensions are presented for existing fractals with adjacent contractions constructed based on the Catalan solids.
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Scientific article
Computer-Based Testing (CBT) has gained prominence in Nigeria due to its efficiency and scalability in evaluating students across various educational institutions. However, various forms of exam cheating, such as candidate swapping and unauthorised assistance, threaten its integrity. This research explores the application of Convolutional Neural Networks (CNNs) for identity verification in Nigerian CBT environments and presents a CNN-driven facial biometric model based on the findings. The model extracts facial features of examinees from real-time videos of CBT exam sessions, and it compares them with pre-registered data to verify test takers' identities, as well as to detect and report instances of candidate swapping and unauthorised assistance during the ongoing exam. The model is trained on diverse datasets like VGGFace2 and CASIA African Face Dataset to enhance fairness and accuracy for African demographics. This ensures effectiveness in Nigerian Computer-Based Testing (CBT) and local contexts. Evaluation of the model and its comparative analysis with existing systems and other biometric methods were performed. The assessment involved 2,000 genuine and 3000 impostor samples, achieving 99.52% accuracy with high precision and recall of 0.998 and 0.99, respectively. The results demonstrate the model’s high accuracy, low false acceptance, and minimal false rejection rates, and highlight the model’s viability in maintaining exam integrity and accessibility.
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