Unilag Journal of Mathematics and Applications

NEW VARIETIES OF BCI ALGEBRAS

2025-10-31T00:36:54+00:00

A BCI algebra is said to form a variety if it satisfies certain axioms. New varieties of BCI algebras, namely; palindromic, almost palindromic, hyper-palindromic and point-wise palindromic BCI algebras are introduced in this paper. These algebras are characterized by distinct axiomatic configurations. Their algebraic properties are investigated. The relationships that exist between the varieties are discussed. Necessary and sufficient conditions for the transformation of one variety to another are presented. Moreover, given any arbitrary algebras of type (2,0), we present conditions for such algebras to belong to any of the new varieties of BCI algebras.

TWO PARETO OPTIMUM-BASED HEURISTIC ALGORITHMS FOR MINIMIZING TARDINESS AND LATE JOBS IN THE SINGLE MACHINE FLOWSHOP PROBLEM

2025-10-31T00:36:54+00:00

Flowshop problems play a prominent role in operations research, and have considerable practical significance. The single machine flowshop problem is of particular theoretical interest. Until now the problem of minimizing late jobs or job tardiness can only be solved exactly by computationally intensive methods such as dynamic programming or linear programming. In this paper we introduce, test, and optimize two new heuristic algorithms for mixed tardiness and late job minimization in single-machine flowshops. The two algorithms both build partial schedules iteratively. Both also retain Pareto optimal solutions at intermediate stages, to take into account both tardiness and late jobs within the partial schedule, as well as the effect of partial completion time on not-yet scheduled jobs. Both algorithms can potentially be applied to scenarios with hundreds of jobs, with execution times running from less than a second to a few minutes. Although they are slower than dispatch rule-based heuristics, the solutions obtained are far better. We also attempted a neural-network solution which performs poorly, and propose reasons why neural networks may not be a suitable approach.

NUMERICAL COMPUTATION OF CHEMICAL REACTION, HEAT GENERATION, THERMAL RADIATION, AND VISCOUS DISSIPATION EFFECTS ON MAGNETOHYDRODYNAMIC (MHD) CONVECTIVE FLOW THROUGH A POROUS MEDIUM

2025-10-31T00:36:54+00:00

This research explores the effect of viscous dissipation on free convection 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 parameter (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.

WORK PERFORMED BY CLOSED AND CLOPEN M-TOPOLOGICAL FULL TRANSFORMATION SEMIGROUP SPACES MCTn AND Clp(MCTn )

2025-10-31T00:36:54+00:00

Let α and β be two elements of an m-topological transformation semigroup space. In this paper, we introduce and derive explicit formulas for the work performed by elements in the full transformation semigroup M_Tn , the closed m-topological semigroup M_CTn , and its clopen counterpart Clp(M_CTn ), where the displacement of a point x under a transformation α is given by d(x, αx) = |x − αx|. We further establish explicit formulas for the average work and the power within these semigroup spaces. To ensure that the system stabilizes to integer values, we incorporate the floor function [x♩ = {n | n ∈ Z⁺, n ≤ x < n + 1}. Numerical evaluations confirm the validity of the derived formulas and reveal consistent growth patterns, thereby high- lighting new combinatorial properties of m-topological transformation semi- group spaces.

POLICE PATROL OPTIMIZATION: A PROFICIENCY-AWARE MODEL FOR RAPID RESPONSE TO INCIDENTS

2025-10-31T00:36:54+00:00

This study introduces the Crime Neutralization Model (CNM), an optimization based framework designed to improve the strategic deployment of police patrol teams. The CNM addresses critical limitations in traditional rapid response systems by incorporating three, often neglected operational factors: (1) variation in patrol team proficiencies, (2) crime-type-specific resource demands and (3) scenario-dependent severity levels. A discrete mathematical programming approach is employed to minimize the expected weighted response distance, while ensuring that all incidents are covered by suitably proficient teams within defined response radii. The model is validated using synthetic urban crime data, where results demonstrate that 10 patrol teams operating within a 1.5 km response radius achieve a 45.29% improvement in travel distance efficiency. Sensitivity analysis yields two key insights: first, optimal deployment strategies remain consistent across increasing response distances, indicating robustness; second, performance does not scale linearly with team count, most notably, a deployment of 12 teams unexpectedly results in re- duced efficiency. With computation times ranging from 4 to 12 seconds, the CNM offers a practical and adaptive tool for police departments to enhance resource allocation in alignment with both spatial constraints and operational capabilities.

A DERIVATIVE–FREE BLOCK HYBRID METHOD FOR NUMERICAL QUADRATURE

2025-10-31T00:36:54+00:00

We derive a new ninth-order block hybrid method for the numerical solution of systems of differential equations and we compare results of numerical experiments with an already existing method in the literature. Both methods are bye-products of linear multistep methods using the interpolation and collocation approach. We show computationally that in the absence of round-off errors, the solution obtained by solving systems of differential equations by the existing block hybrid method derived by differentiating the continuous scheme at a particular off–grid point is the same as those obtained in the new method which is derivative free. Besides, the new block hybrid method which is derivative free results in a well conditioned system as opposed to the ill–conditioned one in the literature. Therefore, providing an answer to Shampine’s claim that matrices arising from the numerical approximation of stiff initial value problems using Linear Multistep Methods are mostly ill–conditioned. Finally, we showed computationally how an LU- type preconditioned Quasi Minimal Residual with a fixed default tolerance reduced the condition number of the old and new methods, with the latter resulting in the smallest minimum norm of residual.

MODIFIED RUNGE-KUTTA ALGORITHM FOR OSCILLATORY CHEMICAL KINETICS

2025-10-31T00:36:54+00:00

Oscillatory dynamics frequently arise in the kinetics of chemical reactions, posing significant challenges to traditional numerical methods in capturing the dynamics. In this study, we introduce a class of modified Runge- Kutta methods specifically designed to solve such oscillatory chemical kinetics problems. Based on exponential fitting conditions for Runge-Kutta methods, we adapt several classical Runge-Kutta methods to better accommodate oscillatory behaviour. Three distinct classes of these modified methods based on some choosen parameters are proposed and presented. To evaluate their effectiveness, we conduct numerical experiments on two practical problems characterised by oscillatory chemical reactions. The results clearly demonstrate that the modified Runge-Kutta methods outperform their classical counter- parts when applied to oscillatory systems.

NONLINEAR CONVERGENCE DYNAMICS IN FUZZY METRIC SPACES WITH APPLICATIONS TO DECISION-MAKING AND IMAGE PROCESSING

2025-10-31T00:36:54+00:00

This paper examines nonlinear convergence dynamics in fuzzy metric spaces, a framework that incorporates uncertainty into distance measures. We propose a nonlinear iterative scheme with adaptive parameters to establish the existence and uniqueness of fixed points under generalized contractive conditions. Our contributions include four novel theorems, substantiated by meticulous proofs and illustrated with colorful TikZ diagrams, addressing both single and multi-valued mappings. These findings are applied to multi- criteria decision-making, image segmentation, and stability in uncertain systems, highlighting their practical utility.