Programme accreditation by the National Universities Commission (NUC) is the main external quality assurance mechanism in Nigerian universities, but it is periodic and retrospective: weaknesses are usually discovered during the visit rather than before it. This study aimed to develop and evaluate a machine-learning (ML) framework that predicts accreditation outcomes from routinely collected pre-visit indicators so that institutions can remediate deficiencies early. Because programme-level accreditation records are not publicly available, we built a reproducible synthetic panel of 4,321 accreditation visits to 1,515 programmes in 149 simulated universities (2014–2024), with outcomes (full, interim, denied) generated by NUC-style scoring rules. Fifteen indicators covering staffing, curriculum, facilities, library, funding, research and employer rating, together with ownership, discipline and prior status, were used as predictors. Logistic regression (LR), support vector machine, multilayer perceptron, random forest and extreme gradient boosting (XGBoost) were trained on 2014–2021 visits with university-grouped cross-validation and tested on 2022–2024 visits. LR performed best on the temporal test set (accuracy 0.773; macro-F1 0.708, 95% CI 0.669–0.744; area under the curve [AUC] 0.908), exceeding a prior-status rule (macro-F1 0.537). For the binary task of identifying programmes at risk of not receiving full accreditation, LR achieved an AUC of 0.900 and good calibration; the 20% of programmes with the highest predicted risk included 52 of the 53 denied programmes. Proportion of PhD-holding staff and laboratory provision were the most influential predictors. ML-based risk scoring could support continuous, pre-emptive quality monitoring, but validation on real NUC data is required before operational use.
This study investigates the dynamics of Nigerian bank stock prices using an exponential-growth geometric Brownian motion framework. The model extends the classical geometric Brownian motion (GBM) by incorporating a growth-adjustment parameter $k$ in the drift term, allowing it to capture both deterministic long-term growth and stochastic fluctuations. Three Brownian-motion paths are first presented to illustrate the underlying randomness, followed by sample price paths demonstrating how the same growth rate can produce both upward and downward trajectories depending on the shock realizations. A sensitivity analysis is then conducted to assess the effect of $k$ on the simulated paths. The results show that higher values of $k$ amplify exponential growth or decay and increase dispersion in absolute valuation. This framework provides insight into how long-term growth expectations interact with short-term volatility in the Nigerian banking sector.
Conformal mapping is one of the central geometric techniques of complex analysis because it permits a complicated planar domain to be represented by a simpler one while preserving local angles. This paper develops the analytic conditions for conformality from the principal linear part of a differentiable complex mapping, relates the Cauchy--Riemann equations to local rotation and dilation, and presents explicit mappings between standard domains. Particular attention is given to the Joukowski transformation and its constructive action on circular boundaries. Actual mappings are worked out for the upper half-plane and unit disk, for a strip and half-plane, and for circles mapped by the Joukowski transformation into a line segment, an ellipse, and an airfoil-like profile. The derivations are accompanied by graphical realizations and a discussion of potential-flow aerodynamics. The results make explicit the connection between the analytic formula, its critical points, transformed geometry, and the distinction between local conformality and global one-to-one behavior.
