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LYAPUNOV FUNCTIONS AND ASYMPTOTIC EVENTUAL STABILITY FOR IMPULSIVE SYSTEMS WITH NONLINEAR TERMS
No full textThis paper investigates the asymptotic eventual stability of a class of nonlinear impulsive differential equations with impulses occurring at fixed moments. The analysis is conducted within a Lyapunov framework by extending the classical concept of vector Lyapunov functions to a generalized class of piecewise continuous Lyapunov functions suitable for impulsive systems. This approach effectively captures both the continuous system evolution and the discrete effects introduced by impulses. By employing appropriate comparison principles, the behavior of the impulsive system is related to that of corresponding comparison systems, enabling the derivation of tractable stability criteria. Based on this methodology, sufficient conditions guaranteeing asymptotic eventual stability are established in terms of inequalities involving the proposed Lyapunov functions and system parameters. The results obtained extend and improve several existing stability criteria in the literature. In particular, the proposed conditions are less restrictive and applicable to a wider class of nonlinear impulsive differential systems, thereby enhancing the scope and effectiveness of Lyapunov-based methods for the qualitative analysis of impulsive dynamics
FRENCH TEACHERS' USE OF ARTIFICIAL INTELLIGENCE AS A TOOL FOR ENHANCING THE SECONDARY SCHOOL FRENCH STUDENTS' PERFORMANCE IN LAGOS STATE
No full textThis study examines how French teachers in Lagos State use and perceive Artificial Intelligence (AI) tools to improve student performance. Using a survey and interviews with 60 teachers from public and private secondary schools, the research aims to assess current AI usage, its impact potential, and the main barriers to adoption. The study is guided by the Technological Pedagogical Content Knowledge (TPACK) framework. Preliminary findings indicate a nascent adoption of pedagogically rich AI tools, with only 6.7% of teachers using AI Chatbots often/very often, contrasted by a high reliance on basic tools like Google Translate (used often/very often by 68.3% of teachers). This adoption is constrained by significant infrastructural challenges, with Limited access to computers and internet being rated the most significant barrier (Mean Score = 4.85 out of 5). The paper concludes with specific, ranked recommendations for policy and practice to facilitate the effective integration of AI in French language education.
 
OPTIMIZING CARRYING CAPACITY PLANNING FOR SUSTAINABLE TRANSPORT INFRASTRUCTURE: A SPATIAL DISTRIBUTION OF CAR PARKS IN THE UNIVERSITY OF LAGOS, MAIN CAMPUS.
Get PDFEffective parking infrastructure is a critical component of urban transportation systems, especially in land-use-intensive environments such as university campuses. This study assesses the spatial distribution and carrying capacity of car parks at the University of Lagos, Nigeria, in light of increasing vehicular traffic and inadequate parking supply. Using a mixed-method approach, the research integrates geospatial data acquired from aerial imagery, GPS field surveys, and user questionnaires with secondary sources to evaluate parking demand, facility management, and policy frameworks. A total of 70 parking sites with an aggregate capacity of 2,313 vehicles were identified, revealing substantial deficits in supply relative to demand. Key challenges include the absence of centralized management, poor policy enforcement, and a lack of intelligent transport systems (ITS) to streamline usage. Recommendations include implementing a digital parking guidance application, revising spatial allocation standards, and introducing dynamic pricing schemes to optimize utilization. These findings underscore the need for integrated parking strategies that align with smart city goals and sustainable mobility frameworks on university campuses
Optimizing Neural Networks with Linearly Combined Activation Functions: A Novel Approach to Enhance Gradient Flow and Learning Dynamics
No full textActivation functions are crucial for the efficacy of neural networks as they introduce nonlinearity and affect gradient propagation. Traditional activation functions, including Sigmoid, ReLU, Tanh, Leaky ReLU, and ELU, possess distinct advantages but also demonstrate limits such as vanishing gradients and inactive neurons. This research introduces an innovative method that linearly integrates five activation functions using linearly independent coefficients to formulate a new hybrid activation function. This integrated function seeks to harmonize the advantages of each element, alleviate their deficiencies, and enhance network training and generalization. Our mathematical study, graphical visualization, and hypothetical tests demonstrate that the combined activation function provides enhanced gradient flow in deeper layers, expedited convergence, and improved generalization relative to individual activation functions. Quantitative metrics demonstrate enhanced gradient flow, expedited convergence, and improved generalization relative to individual activation functions. Computational benchmarks show a 25%25% faster convergence rate and a 15%15% improvement in validation accuracy on standard datasets, highlighting the advantages of the proposed approach
A Note on Transmuted Exponentiated Inverse Exponential Distribution and Application to Breast Cancer Data
No full textThe Transmuted Exponentiated Inverse Exponential (TEIE) Distribution has been derived using Exponentiated Inverse Exponential (EIE) distribution and the Quadratic Rank Transmutation Map (QRTM). The developed distribution is more flexible and adaptable in modeling data exhibiting different shapes of the hazard function than its sub-models. The mathematical expressions and shapes of the distribution function, probability density function, hazard rate function and reliability function are studied. The parameters of the TEIE distribution are estimated by the method of maximum likelihood. Finally, the TEIE distribution is applied to breast cancer data set and found to have a better fit than the Transmuted Inverse Exponential (EIE) distribution and the Inverse Exponential (IE) distribution
Some New Operations on Picture Fuzzy Multisets
No full textA multiset is an extension of a crisp set in which elements are allowed to occur more than once, enabling the representation of data where frequency or multiplicity is essential. Building upon this, fuzzy multisets introduce a degree of membership to each element, capturing both quantity and uncertainty. Further developments have led to the formulation of picture fuzzy multisets a robust framework that extends picture fuzzy sets. In this paper, we propose some new operations on picture fuzzy multisets by analyzing existing operations on fuzzy sets, and fuzzy multisets, extending these foundations using picture fuzzy logic principles to define operations that maintain the consistency of positive membership, neutral membership, and negative membership and refusal degrees, establishing a set of axioms and properties (such as commutativity, and distributivity) that the operations must satisfy, proving theorems that verify these properties and constructing a detailed numerical example to illustrate and validate the behavior and correctness of the proposed operations. It was shown that the proposed operations are well-defined, internally consistent, and closed under the structure of PFMs. The example demonstrates that the operations handle ambiguity, contradiction, and repetition effectively, making them suitable for applications in multi-criteria decision-making, knowledge representation, and information systems. The new operations significantly broaden the mathematical toolkit available for handling picture fuzzy multisets. They lay a foundation for future research into more complex structures such as picture fuzzy multirelations, aggregation operators, and soft computing models based on picture fuzzy multisets
Comparing Ordinary Least Squares, Ridge, and Lasso Regression for Multicollinearity Mitigation in Linear Models
No full textOrdinary Least Squares (OLS) regression provides unbiased estimates but performs poorly when predictor variables are highly correlated, due to increased variance and model instability. This study compares the effectiveness of OLS, Ridge regression, and the Least Absolute Shrinkage and Selection Operator (LASSO) in mitigating multicollinearity and improving predictive accuracy in linear models. Using academic data of University of Ilorin undergraduate students, Nigeria, we evaluated model performance using Root Mean Squared Error (RMSE), Variance Inflation Factors (VIF), and cross-validation. Ridge regression applies an L₂ penalty to shrink coefficients, while LASSO uses an L₁ penalty that also enables variable selection by setting some coefficients to zero. The results show that Ridge regression achieved the best generalization performance with the lowest test RMSE (0.2358), while LASSO provided a more interpretable model through coefficient sparsity. OLS exhibited overfitting and the poorest generalization due to high multicollinearity. The findings highlight the importance of regularization techniques in regression modeling, especially in high-dimensional data environments. This study offers practical guidance on model selection when predictive accuracy and feature interpretability are essential.an 
An Algorithm for Approximation of Solutions of Nonlinear Split Equality Mixed Problems
No full textIn this paper, we construct an iterative algorithm with a step-size which is independent of the norm of the operators that approximates a common fixed point in: the set of solutions of SEFPP involving η-demimetric maps, the set of common zeros of finite families of inverse strongly monotone maps, the set of common solutions of systems of generalized mixed equilibrium problems, and the set of common fixed points of infinite families of quasi-nonexpansive maps. We establish in real Hilbert spaces, strong convergence of the sequence generated by our algorithm to a solution of the problem under consideration
Actuarial Analysis of Historical Mortality Trends in Nigeria and Their Implications for Annuity Valuation
No full textThis study analyses historical trends and patterns in age-specific mortality in Nigeria and their actuarial implications for annuity valuation. Using secondary data from the United Nations World Population Prospects (2024 revision), the study applied descriptive and trend analysis to age-specific death rates and life expectancy across selected ages from 1960 to 2024. Descriptive statistics, graphical trends, and comparative assessments were used to evaluate improvements in mortality by age and gender. The results show a consistent decline in mortality rates over time, with the fastest improvements observed among children and young adults, and slower reductions among older adults. Female mortality rates remained consistently lower than those of males, reflecting global longevity patterns. These findings indicate that longevity risk is increasing for pension and annuity providers as Nigerians live longer. The study concludes that periodic review of mortality assumptions is essential for accurate pricing and reserving. It recommends integrating actuarial analysis into national mortality monitoring to strengthen the financial sustainability of life-contingent products
NUMERICAL COMPUTATION OF CHEMICAL REACTION, HEAT GENERATION, THERMAL RADIATION, AND VISCOUS DISSIPATION EFFECTS ON MAGNETOHYDRODYNAMIC (MHD) CONVECTIVE FLOW THROUGH A POROUS MEDIUM
No full textThis research explores the effect of viscous dissipation on free con- vection magnetohydrodynamic (MHD) flow through a porous medium over an exponentially stretching surface in the presence of a chemical reaction. The fundamental governing partial differential equations (PDEs) governing the problems are transformed into nonlinear ordinary differential equations (ODEs) using similarity variable. Numerical solutions are then obtained through the shooting method combined six order Runge Kutta Scheme. Maple software is used for the simulation of the problem. The characteristics of boundary layer flow, along with the behaviour near the bounding surface, and the effect of embedded flow parameters on velocity, temperature and concentration profiles are examined and interpreted through graphical illustrations. The findings indicate that an increase in the Eckert number, radiation, and magnetic pa- rameter (M) enhances the temperature profiles, whereas a rise in the chemical reaction parameter, porosity, and Schmidt number reduces the concentration profiles. To ensure accuracy, a comparative analysis between the present results and previously published outcomes for a specific case is performed, revealing strong agreement