International Journal of Mathematical Sciences and Optimization: Theory and Applications

Structure and Classification of Stable Quasi-Idempotents in Finite Transformation Semigroups

2026-03-19T08:09:42+00:00

This article investigates the structure of stable quasi-idempotents ξ of arbitrary defect d(ξ) ≥ 1. We show that, unlike transpositions, stable quasi-idempotents generate the singular transformation semigroups Tₙ\Sₙ and Pₙ\Sₙ, with the inclusion Tₙ\Sₙ ⊆ Pₙ\Sₙ. These semigroups are significant because every finite semigroup is either a subsemigroup or an embedding of them, highlighting the universality of Pₙ. We classify stable quasi-idempotents in terms of their defects and path-cycle structures, establishing explicit enumerative formulas. In particular, a defect-1 stable quasi-idempotent of span s has rank ₙCₛ = n!/((n−s)!s!). This classification clarifies the relationship between stable quasi-idempotents, idempotents, and quasi-idempotents, and provides a framework for analyzing the subsemigroups they generate. Our results connect classical work on transformation semigroups with new enumerative and structural insights.

A Generalized Differential Operator in Function Theory with Applications to Coefficient Bounds of p-Valent Analytic Functions

2026-03-19T08:17:33+00:00

In this paper, a new differential operator that generalizes several well-established operators in geometric function theory by incorporating principles of q-calculus and p-valent analytic functions is introduced. The key objectives include establishing its equivalence to existing operators and deriving coefficient bounds for the associated p-valent function classes. Using q-differentiation and multiplier transformations, we formulate a generalized class of analytic functions and derive coefficient bounds within the unit disk. Numerical comparisons and graphical illustrations reveal that the new operator yields finer results.

A Diffusion-Reaction Model for the Spread and Control of an Infectious Disease: A Case Study of Meningitis Outbreak in Zamfara State, Nigeria

2026-03-19T08:23:33+00:00

Infectious diseases abound in the world, affecting and even claiming the lives of many of their victims. Many researches have been conducted with the goal of proffering how to curtail or control the spread of the diseases. A diffusion-reaction model is herein proposed for the spread and control of an infectious disease. A numerical approach is considered for the solution of the proposed model. With the aid of data generated from an instance of meningitis outbreak, the rate of spread of the disease and the quantity of treatment, to apply to control the disease, are determined.

Comparing Ordinary Least Squares, Ridge, and Lasso Regression for Multicollinearity Mitigation in Linear Models

2026-03-19T08:31:52+00:00

Ordinary 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

2026-03-19T08:37:58+00:00

In 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.

MHD Natural Convection Couette Flow in a Vertical Channel: Effects of Nonlinear Boussinesq Approximation and Suction/Injection

2026-03-19T09:26:00+00:00

This study analytically investigates buoyancy driven magnetohydrodynamic (MHD) natural convection Couette flow in a vertical channel, focusing on the effects of the nonlinear Boussinesq approximation, suction/injection and magnetic fields. The nonlinear Boussinesq term captures significant thermal variations beyond linear models, suction/injection modifies boundary-layer thickness and convective transport, and the magnetic field introduces Lorentz-force damping in electrically conducting flows. The governing momentum and energy equations are solved using the Homotopy Perturbation Method (HPM), and the influence of various parameters on velocity and temperature distributions is examined. Results indicate that the nonlinear Boussinesq parameter enhances fluid motion near the moving plate while suppressing it near the stationary plate. Increased Hartmann numbers uniformly dampen velocity due to stronger Lorentz forces, whereas suction/injection modulates flow development by adjusting the boundary layer. The findings highlight the interplay of buoyancy, magnetic suppression and boundary layer control, providing insights for optimizing flow stability and heat transfer in advanced thermal fluid systems.

On the Monoid Generated by Newton Algorithm in Solving a Particular Cubic Polynomial

2026-03-19T09:29:58+00:00

We initiate the study of the algebraic interpretations of the Newton algorithm via transformation semigroup. We use MATLAB to solve the equation x³ + 4x² - 10 = 0 with an error tolerance of ε = 10⁻⁴. In each iteration, we obtain a transformation on a set of seven elements. With the aid of GAP 4.0, we construct a monoid that interprets the algebraic phenomena of all the iterations. The study reveals that the monoid obtained is left-adequate with 64 elements.

The Construction and Reconstruction of the Neutrosophic Hom-Groups and Neutrosophic Hom-Subgroups from the Indigenous and Primitive Hom-Group

2026-03-21T20:07:25+00:00

Hom-groups are the non-associative generalization of a group whose associativity and unitality are twisted by a compatible bijective map. The neutrosophic set is a powerful tool in dealing with incomplete, indeterminate and inconsistent data that exist in the real world. Neutrosophic set is characterized by the truth membership function in the set (T), indeterminacy membership function in the set (I) and falsity membership function in the set (F) where 0 ≤ T + I + F ≤ 3. In this work, we have been able to give some introductory entities on the concept of both Hom-groups as well as the neutrosophic Hom-groups; our utmost aim is to construct neutrosophic Hom-group and neutrosophic Hom-subgroups from the already known Hom-groups.

A Note on the Test of Equality Between Two Bivariate Groups: An Analogue to Kolmogorov-Smirnov Test Statistic

2026-03-19T09:40:57+00:00

This study developed parametric and nonparametric test statistic, an analogue to Kolmogorov-Smirnov two sample test, for the testing of the equality between bivariate groups. We also established the performance of the developed test statistic in achieving accurate separation and classification. The concept layout model, which is based on Cartesian interaction between discrete random variables (rv's) xₘ and yₖ arranged in rows and columns respectively for m, k ∈ ℕ, has a behavioural pattern with bivariate cumulative distribution function (cdf) F(x,y). We assumed that the content within the matrix m × k frame followed log-logistic distribution (LLD) and is distribution free. The test statistic t' is the absolute difference between two bivariate cdf, |F₁(x,y) - F₂(x,y)|, under the two distribution scenarios. We then optimize the test statistic which is a function of relationship matrices from the two groups and established its significance at optimal parameter value, from a newly introduced multivariate test significance, before investigating its performance analysis. This analysis enhances the understanding of the profiled content in the two groups, whether they are from the same group or not. In addition, we established the discrimination accuracy of the relationship matrix model towards perfect classification (diagnostic). Application to the discrimination and classification of Bumpus, cancer and mode of delivery data were established.

An Analytical Investigation of MHD Williamson Fluid Flow over an Inclined Stretching Sheet in a Porous Medium with Non-Uniform Internal Heat Generation and Mixed Convection

2026-03-19T09:48:38+00:00

The complex interplay between heat transfer, fluid motion, and porous media permeability plays a pivotal role in numerous physical and engineering applications. In particular, the control of heat generation and absorption under mixed convection has garnered considerable attention due to its relevance in thermofluid systems embedded in permeable structures. This research presents a semi-analytical approach for solving the nonlinear Williamson fluid model, accounting for the combined effects of mixed convection, medium permeability, and non-uniform heat generation. Through similarity transformations, the governing partial differential equations are reduced to a system of ordinary differential equations, which are subsequently solved using Legendre polynomials as basis functions and Gauss-Lobatto collocation points. The resulting algebraic system is handled in Mathematica 11.0, with solution accuracy verified by comparison to results from the classical Runge-Kutta shooting technique. Numerical findings reveal that increasing the Grashof number enhances fluid velocity, while higher porosity intensifies thermal fields but suppresses flow due to increased resistance in the porous medium. Moreover, spatially varying heat generation induces steep thermal gradients, potentially leading to localized thermal stresses. The proposed methodology proves effective for analyzing complex nonlinear fluid dynamics, offering robust insights for applications in energy systems, geophysical flows, and thermal engineering.