| 1 |
Author(s):
Thomas Adidaumbe Ugbe, Richmond Ofonodo, Edet Effiong Bassey, Stephen Sebastian Akpan.
Page No : 1-14
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On Constrained Programming Problems with Singular Designs via Super Convergent Line Series.
Abstract
The study extends the Super Convergent Line Series Algorithm to a case where the determinant information matrix of the design is zero by employing the Moore-Penrose inverse approach. The algorithm is tested using a numerical example on a constrained programming problem. The optimal solution obtained by the algorithm compares favorably with the one obtained by an existing Frank-Wolfe method and the value of the optimizer satisfies the given constraint equation.
| 2 |
Author(s):
Sekou Mohammed Kamara.
Page No : 15-30
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Understanding Long-Term Share Price Behavior of Jubilee Holdings Limited on the Kenya Securities Exchange: A Markov Model Approach Complemented by Ergodicity and Stationarity.
Abstract
This paper investigates the long-term behavior of Jubilee Holdings Limited’s share price by employing a Markov model to conduct a state-based analysis of its daily returns. The state space is defined by three states: Positive, Negative, and Zero. The Markov model results indicate long-term probabilities of 31.2% for a positive return, 30.0% for a negative return, and 38.8% for zero return. Additionally, the study incorporates the concepts of ergodicity and stationarity to assess the magnitude of the daily returns through drift analysis. The drift analysis further reveals that the ensemble mean of the daily returns of the share price is zero, as confirmed by a Z-test. These findings suggest that the share price demonstrates long-term stability, with no sustained directional movement. While this analysis focuses on capital gains, it highlights Jubilee Holdings Limited’s consistent dividend payments in recent years as a consideration for income-focused investors.
| 3 |
Author(s):
Chacha Paul Jackson, Argwings Otieno (Ph.D.), Julius Koech (Ph.D.).
Page No : 31-46
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Vector Autoregression Modeling of Malaria Incidence and Mortality Rates in Migori County, Kenya: A Time Series Analysis Incorporating Exogenous Influences.
Abstract
Malaria remains hyperendemic in Kenya’s Lake Victoria basin despite scalable interventions. It is a pressing public health challenge in Migori county that reported 27% mortality rate in 2020 in children aged 6-59 months, far exceeding national levels. Reports indicate different contributing factors to malaria dynamics in Migori county, including marginal insecticide-treated net (ITN) use, ITN access, effective anti-malaria treatment, and prevalence of malaria infection. The present study seeks to elucidate the temporal interaction between malaria incidence and mortality by employing a range of time series analyses, incorporating exogenous influences, by applying classical vector autoregressive (VAR) model to capture lagged dependencies. Further, the study invoked a Bayesian VAR (BVAR) after incorporating exogenous variables for parameter estimating, utilizing Monte Carlo simulations and Gibbs sampling. For model adequacy and forecast accuracy, the analysis made use of Ljung-Box test, partial autocorrelation function, autocorrelation function (ACF), and normality tests among other diagnostic tests. The hierarchical Bayesian vector autoregressive model (BVARX) incorporates monthly incidence and mortality rates (2014-2024, n=120) as the endogenous variables. The exogenous variables comprised ITN access and use, treatment efficacy, and infection prevalence. Ward-level heterogeneity summed the spatial random effects. Hamilton Monte Carlo model estimation with convergence assessed using R ̂<1.01 Counterfactual simulations quantified intervention impacts. ITN use reduced incidence (β = −1.43, 95% CrI: −2.21, −0.65) but access increased mortality (β = 1.81, CrI: 0.32, 3.30), suggesting behavioral misuse. VARX outperformed VAR (WAIC: 412 vs. 587), yet residual spatial autocorrelation (Moran’s I = 0.34, *p* = 0.01) indicated unobserved confounders. BVARX forecasts predicted 22% (CrI: 18–27%) higher incidence by 2025 under current interventions. The regression analysis identified that higher ITN use is significantly associated with reductions in both malaria mortality and incidence. While ITNs and treatments show efficacy, their benefits are eroded by suboptimal utilization and ecological feedbacks. The study recommended the use of ward-level VARX outputs for geospatial targeting of ITN campaign as well as integrated resistance monitoring through adaptive Bayesian frameworks.
| 4 |
Author(s):
Okon Emmanuel A., Ugbe Thomas A., , Akpan Stephen S..
Page No : 47-65
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Seven-Factor Central Composite Design Robust to A Pair of Missing Observations.
Abstract
Seven-factor central composite design has been studied with respect to a pair of missing observations. The central composite designs comprise of factorial, axial and center parts. All possible combinations of the missing points are considered. The study is based on the criterion of minimizing the maximum loss, which depends mainly on the number of factors involved in the experiment, the distance of the axial point from the design centre ( ) and position of the missing points.
The work considered the case of minimizing the maximum loss when two observations are missing in a Central Composite Design (CCD) with k =7. The loss of every possible combination of two missing observations was calculated using minimax loss criterion, and groups of two missing observations producing same losses formed. The process was repeated for a range of values to locate the for which the maximum loss is minimum. It was discovered that the loss effect of missing a pair of factorial points is a decreasing function of increasing , while the loss effect of a pair of axial points is a decreasing and increasing function of increasing . The loss effect of missing a factorial and axial point has no specific direction of increase or decrease on increasing values. It was also discovered that irrespective of the value of k, when a couple of a pair of observations is missing the design will breakdown.
| 5 |
Author(s):
Peter Chimwanda, Edwin Rupi.
Page No : 66-72
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A Multivariate Approach to Understanding Trait Interactions in Soybean Plants.
Abstract
Despite widespread use of statistical methods, advanced techniques like multivariate analysis are often underutilized, a trend that can lead to methodological missteps. This article focuses on Multivariate Analysis of Variance (MANOVA) and its necessary follow‑up procedures, addressing why MANOVA often remains overlooked. We review its conceptual foundation, analyzing multiple dependent variables collectively rather than separately, as in ANOVA, and illustrate its advantages, particularly the reduction of Type I error and the ability to detect multivariate patterns unnoticed in univariate analysis. Drawing on a practical case study involving a 2025 Kaggle soybean dataset (55,450 records across 13 agronomic traits), we apply MANOVA (via Jamovi) across 36 treatment combinations of genotype, salicylic acid, and water stress. Multivariate tests (Pillai’s trace, Wilks’ lambda, Hotelling’s trace, and Roy’s largest root) were all highly significant (p < 0.001), indicating group-level differences across variables. Subsequent univariate ANOVA revealed significance for each trait, and post‑hoc pairwise comparisons (630 total) identified numerous significant differences. Finally, mean comparisons highlight the S1C3G3 group as top-performing across multiple key metrics. Our findings demonstrate the value of MANOVA in agricultural research and recommend adopting genotype 3 with salicylic acid at 450 mg under minimal water stress.
| 6 |
Author(s):
Okeke Ngozi Christy, Olanrewaju Samuel Olayemi, Mohammed Zubairu Anono.
Page No : 73-95
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Robust Estimation in Simultaneous Equation Models Addressing Multicollinearity and Heteroscedasticity through Adaptive Penalized GMM Techniques.
Abstract
This study develops and evaluates robust estimation techniques for simultaneous equation models (SEMs) under conditions that violate the classical linear regression assumptions specifically multicollinearity, and heteroscedasticity. Building on limitations identified in conventional estimators such as Two-Stage Least Squares (2SLS), Three-Stage Least Squares (3SLS), and Full Information Maximum Likelihood (FIML), we propose five novel estimators: Adaptive Ridge IV (ARIV), Generalized Two-Stage Adaptive Elastic-Net (G2SAE), Elastic-Net IV (ENIV), Heteroscedasticity-Consistent Generalized Method of Moments (HCGMM), and Three-Stage Adaptive Elastic-Net (3SAEN). The performance of these estimators were assessed using extensive Monte Carlo simulations across varying degrees of multicollinearity, heteroscedasticity, and sample sizes (n = 30, 50, 100, 200), with 2,000 replications for each scenario. Evaluation metrics include Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Bias. The results reveal that the proposed estimators consistently outperform traditional methods, especially under severe assumption violations. HCGMM emerges as the most robust and efficient estimator, exhibiting the lowest RMSE and bias across nearly all conditions, including small sample sizes. G2SAE and 3SAEN also demonstrate strong asymptotic properties and adaptability to complex data structures. In contrast, traditional estimators particularly 2SLS and 3SLS exhibit significant performance deterioration in the presence of heteroscedasticity and multicollinearity. A comparative analysis further highlights a trade-off between computational efficiency and estimation accuracy, with the proposed methods offering a favorable balance. These findings have practical implications for econometric modeling in applied research, particularly in fields where data irregularities are prevalent. The study underscores the need for methodological reform and adoption of robust estimation techniques to improve the reliability of policy-relevant empirical analysis.
| 7 |
Author(s):
Dismas Raimbas, Mohsen Aghaeiboorkheili.
Page No : 96-112
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Impact and Collision Dynamics Modeling and Simulation for Road Safety in Papua New Guinea.
Abstract
This project explores the mathematical modeling of impact and collision dynamics with a focus on enhancing vehicle and road safety in Papua New Guinea (PNG). Using fundamental principles from classical mechanics - particularly the impulse-momentum theorem, conservation of momentum, and kinetic energy analysis - this study demonstrates how real-world vehicle collisions can be analyzed and predicted through mathematical equations. A central scenario models a 1000 kg car decelerating from 20 m/s to rest, showing how varying the impact duration significantly changes the force experienced: a crash over 0.2 seconds results in a 100,000 N force, while extending that to 0.3 seconds reduces the force to 66,667 N. These calculations highlight how small changes in crash parameters, modeled mathematically, have major effects on safety outcomes. This mathematical framework provides a low-cost, accessible alternative to physical crash testing, making it especially valuable in PNG where safety infrastructure and testing resources are limited. The project reinforces the role of applied mathematics as a powerful tool in engineering design, public safety planning, and real-world problem-solving.
| 8 |
Author(s):
Hazel Kiap, Mohsen Aghaeiboorkheili.
Page No : 113-124
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The Foundation of Electromagnetism: A Comprehensive Study of Maxwell’s Equations.
Abstract
In the history of physics, one of the deepest integrations that classically combined the phenomena of magnetism, optics and electricity into one theoretical structure is represented by Maxwell’s equations. This analysis gives a thorough mathematical formulation of the four fundamental equations elegantly. It provides a deeper understanding beginning from their historical basis in the works of Faraday, Gauss and Ampère and finishing in Maxwell’s vital input – the displacement current. We illustrate how these four equations beautifully surface from experimental laws when united with advanced vector calculus via comprehensive mathematical analysis.
A disclosure that changed the concept of light is a consequence of Maxwell’s equations which has surpassed classical electromagnetism that led immediately to the forecast of electromagnetic waves. James C. Maxwell, when synthesizing magnetic and electricity, he has proven that light alone is an electromagnetic phenomenon. Today, in this modernized world, Maxwell’s equation has become the basis for electronic and electrical engineering. Nevertheless, examined here are some of their restrictions, notably in relativistic contexts and quantum mechanical where more enhanced theories become crucial. This analysis goals to give both thorough mathematical treatment and a well-defined understanding of the foundation equations of theoretical physics.
| 9 |
Author(s):
Florence Palin, Benson Mirou, Mohsen Aghaeiboorkheili.
Page No : 125-135
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Analysis of Healthcare System Towards Improvement.
Abstract
This research aims to analyse the current health system at the Papua New Guinea University of Technology (PNGUOT) clinic, by identifying ways to improve the healthcare services for students and staff. The clinic provides for the university community and the surrounding population. However, the clinic faces several challenges. The results reflect more widespread issues faced by healthcare facilities in Papua New Guinea, where infrastructural limitations can affect effective service delivery. This study provides actionable recommendations better to meet the evolving health needs of its users.
| 10 |
Author(s):
Akingbade James Akinsuyi, Bamigbola O. M..
Page No : 136-161
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Transmission Dynamics and Control of a Deterministic Bird-Human Avian Influenza Model.
Abstract
This paper develops a deterministic model to analyze the transmission dynamics and control measures of avian influenza, with a specific emphasis on bird-to-human transmission. The model innovatively integrates key intervention measures, including vaccination, treatment, and quarantine, while categorizing the human population into seven distinct classes and the bird population into four. A dynamic analysis is conducted to elucidate the epidemiological characteristics and potential control measures for avian influenza outbreaks. The qualitative properties of the model are rigorously assessed using the Jacobian matrix, and the basic reproductive ratios are calculated utilizing the next-generation matrix approach. A stability analysis of the equilibrium states is performed through the trace and determinant of the Jacobian matrix, revealing the existence of two key equilibria: the disease-free equilibrium and an endemic equilibrium. Simulation experiments show that the synergistic application of all three control measures significantly reduces infection rates compared to the implementation of individual or paired strategies. Furthermore, a sensitivity analysis highlights the most influential parameters affecting control outcomes, enhancing the understanding of effective management strategies. This research provides valuable insights into managing avian influenza transmission, contributing to the broader discourse on infectious disease control in avian and human populations.
| 11 |
Author(s):
Adeoye Adebola Samuel, Adeoye Tolulope Olamide, Owoeye Adetola Sunday.
Page No : 162-185
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Dynamic Influence of Foundation Stiffness on Rectangular Structural Plate with Constant Bi-parametric Elastic Foundation with Simple Elastic End Conditions.
Abstract
This paper considers the dynamic influence of foundation stiffness such as foundation modulus, shear modulus, Young modulus as well as rotatory inertia correction factor on the vibrations of orthotropic rectangular structural plate resting on a constant bi-parametric elastic foundation with simple elastic end conditions when moving distributed loads are traversing on the structural plate. The orthotropic rectangular structural plate model is a coupled fourth order partial differential equation with variables and singular coefficients. The solutions to the model are obtained by transforming the fourth order partial differential. The fourth order partial differential equation is transformed to a set of coupled second order ordinary differential equations by using a special technique adopted by Shadnam et al [11]. This set of second order ordinary differential equations is then simplified using modified asymptotic method of Struble. The closed form solution is analyzed, resonance conditions are obtained and the results are presented in plotted curves to show the impact of foundation parameters for both cases of moving distributed mass and moving distributed force.
| 12 |
Author(s):
Umoh Uduak David, Usoro Anthony Effiong.
Page No : 186-203
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Comparative Analysis of the Impact of Some Economic Variables on Inflation Rates in Nigeria using Robust Regression.
Abstract
This study compares the performances of ordinary least squares(OLS) and some robust regression estimation methods in the presence of outliers, as they are applied to examine the impact of economic variables (FDI, Money Supply, GDP per Capita, Population Growth and Real Interest rate) on Inflation rates in Nigeria over the period, 2006 to 2023. The Robust Regression methods adopted are M-estimation, Bi-square Estimation, Iteratively Re-weighted Least Squares (IRLS), S-Estimation. Based on the analysis, it is found that M-estimation and Iteratively Re-weighted Least Squares (IRLS) give similar result as Bi-square robust estimation method as the most appropriate methods, since they give the least standard error of residuals and higher coefficient of determination (). This is followed by S- estimation, while OLS performs the worst. From the results of OLS regression it is found that Money Supply shows a positive significant impact on inflation rates, while Real Interest Rates shows a negative significant impact on inflation rates.. Robust regression estimation method using bi-square estimation(M- estimation, IRLS) methods indicates that money supply shows significantpositive impacts on inflation rates; while GDP per capita and real interest rate shows negative significant impact on inflation rates. S-robust regression analysis method showed that FDI, GDP per capita, population growth rates and real interest rates have negative and significant impacts on inflation rates.
| 13 |
Author(s):
Ubong D. Akpan.
Page No : 204-212
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Analysis of Fractional Input Stability and Global Asymptotic Stability of Systems of Fractional Differential Equations.
Abstract
Fractional input stability and global asymptotic stability of systems of fractional differential equations have been studied in the sense of Caputo. Systems of fractional differential equations have been studied using Lyapunov method and other known stability notions. Two stability theorems have been stated and proved. Examples are given to demonstrate the utilization of the theorems.
| 14 |
Author(s):
Gyobe A., Adeloye T. O., Adeoye A. S..
Page No : 213-232
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Dynamic Response of a Non-Uniform Rayleigh Beam Under Accelerating Distributed Masses on a Bi-Parametric Elastic Foundation.
Abstract
This study investigates the problem of a non-prismatic Rayleigh beam subjected to moving loads with arbitrarily prescribed velocities. The research addresses a complex structural dynamics problem that has significant implications for various engineering applications, including railway systems, bridge structures, and industrial machinery where moving loads interact with flexible structural elements. The non-uniform Rayleigh beam model incorporates both translational and rotational inertia effects, providing a more accurate representation of real-world structural behaviour compared to classical Euler-Bernoulli beam theory. The beam's non-uniformity is characterized by spatially varying material properties and geometric parameters, which significantly influence the dynamic response patterns. The bi-parametric elastic foundation is modelled using Winkler and Pasternak foundation parameters, accounting for both normal and shear interactions between the beam and its supporting medium. The accelerating distributed masses represent a realistic loading scenario encountered in many practical applications, where the velocity and acceleration of moving loads vary continuously along the beam span. This loading condition introduces complex inertial effects and coupling between the beam's natural vibration modes and the motion characteristics of the distributed masses. Gerlakin's weighted residual method is employed to treat this vibrating system problem, as it was in the preceding section. This technique is first used to transform the fourth-order partial differential equation with singular and variable coefficients governing the motion of this vibrating beam. The resulting system of equations called Gerlakin's equations is further simplified using asymptotic method of Struble to obtain a second order ordinary differential equation which is then solved using Duhamel integration method.
| 15 |
Author(s):
Lawal Fatai Kolade, Olumi Toba Timothy, Akor Enejo Felix, Mathias Ahiaba, Kabir Jamiu.
Page No : 233-246
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Comparability of Two Stochastic Models in the Analysis of the Nigerian Female Mortality.
Abstract
The study examine the strength of two stochastic models, the Lee Carter model and Functional Data Time Series Analysis in modelling Nigeria Female Mortality. The data used for the analysis were obtained from Nigeria Bureau of Statistics from 1998-2024. Based on various errors of measurement, it was discovered that the Functional Time series Data Analysis (FDTA) performs better in the modelling of Nigeria Female Mortality.
| 16 |
Author(s):
Ijeoma E. Nwachukwu.
Page No : 247-254
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Topological Isomorphism of the Space of Fréchet Generalised Functions.
Abstract
The characterisation of the space of Fréchet generalised functions was established with respect to the weak-⋆ topology, which confirms the completeness of the space, G_X, through the space of test functions , D(X). The isomorphism bridges the gap between the Fréchet space of test functions and the space of generalised functions.
