Asian Journal of Pure and Applied Mathematics

Quasi S-Menger Spaces and Fixed-Point Theorems via Rational Inequalities with Applications

Neeraj Malviya, Pradip Kumar Keer — Tue, 13 Jan 2026 00:00:00 +0000

S-metric space is a comparatively new concept in the novel and presently there is much attention being given to the abstraction of S-metric and fixed-point theory in these spaces. The concept of S-Menger spaces was popularized in the novel as an abstraction of both S-metric space and Menger spaces. In the present paper, we define quasi-S-Menger space and prove fixed-point theorems for rational inequality in S-Menger space. Some applications are also given is support of our results. Our results extend the results of Gupta et al. (2013) in the setting of S-Menger space.

Interconnections among Radio Number, Clique Number and Chromatic Number

S. Vimalajenifer — Thu, 15 Jan 2026 00:00:00 +0000

Let \(G(V,Ε)\) be a simple, connected and undirected graph. A radio labeling of G, \(ψ:V→{1,2,3,…} \) is a function satisfying the condition for any two distinct vertices u and v that: \(d(u,v)+|ψ(u)-ψ(v)|≥1+diam(G), \) where d(u, v) denotes the distance between the vertices u and v and diam(G) denotes the diameter of the graph G. The of a radio labeling is the maximum integer that assigns to a vertex and radio number, rn(G) is the minimum span taken overall radio labelings of G. This paper presents some bounds connecting radio number with clique number and the chromatic number. In addition, the possible constructions of simple connected graphs with radio number as the algebraic sum of clique number and a non-negative integer. Also, graph with radio number equal to the algebraic sum of chromatic number and a non-negative integer.

Bridging Theory and Application in Modern Mathematics: Insights from AI, Epidemiology, and Sustainability

Onome Festus Ohwojeheri, Friday Z. Okwonu — Tue, 27 Jan 2026 00:00:00 +0000

This study examines emerging branches of mathematics, focusing on how theoretical constructs are transformed into practical applications across contemporary fields. It is a review‑based analysis that synthesises mathematical theories and their applications across artificial intelligence, epidemiology, and sustainability. The research aims to: (1) trace major directions in modern mathematical development and their practical implementations, and (2) analyse how theoretical advancements evolve into applied methodologies. A mixed‑methods approach is employed, combining a qualitative review of scholarly literature (2010–2025) with quantitative demonstrations using mathematical modelling and numerical simulations. Applications in artificial intelligence, epidemiology, and sustainability are explored to illustrate the growing reliance on algebraic structures, optimisation techniques, and differential equations. Recent studies also highlight the integration of artificial intelligence with epidemiological modelling and public‑health analytics. The findings underscore mathematics as a central interdisciplinary tool for addressing global challenges such as pandemics, climate change, and technological innovation. The mathematical equations and simulations presented are illustrative, serving to demonstrate key concepts rather than introduce new theoretical developments. Overall, the study emphasises the reciprocal relationship between theoretical progress and the development of implementable solutions to complex real‑world problems.

Sensitivity Analysis of an Age-Structured Model of HIV/AIDS Transmission Dynamics in Nigeria through Mathematical Modelling

Wed, 04 Feb 2026 00:00:00 +0000

This study focuses on the estimation of parameters and sensitivity analysis of an age-structured model of HIV/AIDS transmission dynamics in Nigeria. The two age groups considered are people between 15 to 60 years old (mature susceptibles) and those less than 15 years old (immature susceptibles). Python software was used in the analysis. Sensitivity analysis reveals that the disease transmission rate (β) is the most influential parameter, positively affecting the basic reproduction number, while natural and AIDS-related death rates exert the strongest negative influences. Numerical simulations show a significant decline in susceptible populations, indicating high infection risk. The population of unaware infectives remains higher than that of aware infectives, highlighting a critical hidden reservoir for ongoing transmission. These findings underscore the importance of reducing transmission rates and increasing case detection through awareness campaigns. Hence, urgent intervention such as prevention and control measures are critically needed to mitigate the spread of the infection.

Fuzzy Soft Prenormal Operators

A.M. Nyongesa, Victor Wanjala — Wed, 04 Feb 2026 00:00:00 +0000

This paper introduces and systematically investigates a novel class of operators called fuzzy soft prenormal operators (FSP) within the framework of fuzzy soft Hilbert spaces. Motivated by the need to extend classical operator theory to handle uncertainty and imprecision, we develop this class as a meaningful generalization of fuzzy soft normal operators. We establish several fundamental properties and characterizations, demonstrating that FSP operators preserve essential spectral features while offering enhanced flexibility in modeling operator behavior under fuzzy and parametric uncertainty. Key results include: the closure properties of FSP operators under addition and multiplication under specific commutation conditions; the invariance of the FSP property under translation by scalar multiples of the identity; topological closure in the strong operator topology; and the significant theorem that every fuzzy soft isometry satisfying the FSP condition is necessarily unitary. Furthermore, we explore the relationships between fuzzy soft prenormal operators and other established classes such as fuzzy soft normal, self-adjoint, and unitary operators. The theoretical contributions presented here not only enrich the landscape of fuzzy soft operator theory but also provide a robust foundation for potential applications in mathematical physics, engineering, and decision-making under uncertainty.

A Note on Fractional Semigroup Theory and Fractional Evolution Equations

Wed, 18 Feb 2026 00:00:00 +0000

This paper considers fractional semigroup theory and fractional evolution equations. First and foremost, we present some fractional semigroups and prove the semigroup property associated with Riemann-Liouville fractional integral operator which is not necessarily true for the fractional differential operator. Consequently, we utilize the fractional \(\beta\)-semigroup of operators to solve the fractional abstract Cauchy problem.

Integration of Topological Data Analysis with Machine Learning: For Enhanced Features Representation and Predictive Performance

Samuel Esokpor, John N. Igabari — Wed, 25 Feb 2026 00:00:00 +0000

The Integration of Topological Data Analysis (TDA) with Learning (ML) algorithms provides a welcoming approach for the improvement of feature representation and predictive performance. TDA applies concepts from algebraic topology, specifically persistent homology, to capture the intrinsic shape and connectivity of complex datasets, producing noise-resistant and invariant features. This study reviews core TDA methods, examines their data descriptors, and evaluates their strengths and limitations in comparison with traditional approaches. A structured methodology is developed, encompassing step-by-step TDA feature extraction, ML model selection, and a unified integration workflows. Using both synthetic and real-world datasets, performance is assessed for TDA only, ML only, and integrated TDA–ML pipelines. Implementations are carried out in Python, with models compared on accuracy and computational efficiency. Finally, Results show that TDA–ML integration often outperforms traditional ML, particularly in high-dimensional or noisy environments where topological structure is informative. While computational complexity and parameter sensitivity pose challenges, the Integration of TDA with ML algorithms offers a reproducible framework for practical applications in domains such as bioinformatics, image recognition, and network analysis.Using synthetic datasets generated with known geometric and topological structures, TDA, specifically Persistent Homology was applied to extract shape-based features, which were then combined with standard ML features for training Support Vector Machines (SVM), Random Forests (RF), and K-Nearest Neighbour (K-NN) models. The study showed that models augmented with TDA features significantly outperformed those relying solely on geometric data. Accuracy improved from 0.79 to 0.95, with similar gains in precision, recall, and F1-score. This confirmed that TDA captures structural patterns missed by conventional feature engineering, thereby enabling more effective and interpretable machine learning models.

Numerical Sensitivity Analysis of Diffusion Coefficients under Optimized Lipschitz Perturbations in Functional Spaces

Okeke Ikenna Stephen, Ezeaka Vincent Ikenna, Orji Samuel Chukwuemeka — Thu, 26 Feb 2026 00:00:00 +0000

Diffusion processes play a fundamental role in chemical, biological, and physical systems, with thermal diffusivity governing heat propagation under temperature variations. The Arrhenius relation links activation energy to reaction rates, providing a quantitative framework for studying temperature-dependent diffusion. This work investigates the Lipschitz stability of heat diffusion models with respect to both the diffusion coefficient and the activation energy. Using a one-dimensional heat equation, an analytical solution via separation of variables is derived, with the diffusion coefficient expressed in Arrhenius form. By applying the Mean Value Theorem, we establish bounds on the solution differences corresponding to variations in diffusion parameters, proving that the solution is Lipschitz continuous with respect to the diffusion coefficient. Extending this analysis to the activation energy, we demonstrate that small perturbations in the activation energy, Q lead to proportionally small changes in concentration, confirming the model’s robustness under parameter uncertainties. Numerical simulations illustrate that diffusion coefficients and concentrations remain bounded for realistic ranges of temperature and activation energy, supporting the theoretical findings. The results highlight the reliability of Arrhenius-based diffusion models for practical and industrial applications, including thermal transport, biomedical modelling, and corrosion studies. This work provides a rigorous mathematical foundation for the sensitivity analysis and stable numerical simulation of diffusion-driven processes under physically relevant parameter variations.

Numerical Study for Higher Order Non-linear Boundary Value Problems Using Laplace Decomposition Method

Thu, 26 Feb 2026 00:00:00 +0000

This paper presents a numerical approach for solving higher-order nonlinear boundary value problems using the Laplace Decomposition Method (LDM). The method, constructed by combining the Laplace transform with the Adomian decomposition technique, allows the governing equations to be handled without linearization or the introduction of small parameters. To demonstrate the applicability of the approach, we consider nonlinear boundary value problems of twelfth, thirteenth, and fourteenth orders. For each problem, approximate series solutions are obtained and compared with known exact solutions and results available in the literature. The numerical results show that the proposed method yields accurate approximations with rapid convergence across the computational domain. All computations are carried out using Maple 2022, confirming that the method is both reliable and computationally efficient for higher-order nonlinear boundary value problems.

Application of Piezoelectric Properties in Understanding Voltage Generation, Displacement, and Acceleration via Packed Sickle Cell

K. W. Bunonyo, Benneth Peter, A. B. Okrinya — Thu, 26 Feb 2026 00:00:00 +0000

Sickle cell disease (SCD) is a hereditary haematological disorder characterised by the synthesis of an abnormal form of haemoglobin, haemoglobin S (HbS). This study derives and analyzes a mathematical modeling of voltage generation, cell displacement, and acceleration using the piezoelectric properties of sickle cells. Blood is an electrically active biological fluid whose mechanical and electrical properties depend strongly on the behavior of its cellular components. In sickle cell disease (SCD), red blood cells undergo structural deformation and reduced deformability, which significantly alter blood flow dynamics, ion transport, and electrical characteristics. Understanding these effects is essential for the development of low-cost and non-invasive diagnostic approaches, especially in regions with limited access to advanced medical facilities. The main objective of this study is to formulate and examine a mathematical model describing the coupled mechanical and electrical responses of packed sickle red blood cells under physiological flow conditions. The model incorporates piezoelectric constitutive relations, mechanical stress, and electrical charge generation arising from cell motion and deformation. The governing equations were derived using Newton’s laws of motion and Kirchhoff’s voltage law, transformed into a state-space form, and solved analytically. Numerical simulations were performed using Wolfram Mathematica version 12 to evaluate the effects of stiffness, noninvasive constant, applied force, and number of sensors. The results showed that cell displacement and acceleration increase with Reynolds number and applied force but decrease with increasing stiffness. Voltage generation rises with increasing turbulence, stiffness, and external force, confirming strong electromechanical coupling. These findings highlight the potential of voltage-based bioelectrical techniques for noninvasive diagnosis and monitoring of sickle cell disease.

Fredholm Integro-Differential Equations: Numerical Solution Using Collocation Approximation

Ojo Olamiposi Aduroja, Ganiyu Ajileye, Adewole Mukaila Ajileye — Fri, 06 Mar 2026 00:00:00 +0000

This paper presents an efficient numerical technique for the solution of high-order Fredholm integro-differential equations using Laguerre polynomial approximation. The given equation is first transformed into an equivalent integral formulation and subsequently discretized into a system of algebraic equations using standard collocation points. The resulting algebraic system is solved via matrix inversion to obtain the unknown coefficients. These coefficients are then substituted into the Laguerre polynomial expansion to generate the approximate solution. Numerical examples are provided to validate the accuracy and effectiveness of the proposed method. The results indicate that the method compares favorably with existing techniques and, in several cases, yields highly accurate approximations to the exact solution.

Numerical Investigation of MHD Casson Nanofluid Blood Flow with Thermal Radiation in a Dilated Stenotic Artery Using Alumina and Ferric Oxide Nanoparticles

T. M. Asiru, A. J. Babatunde, S. O. Sangoniyi, L. O. Adebimpe — Mon, 09 Mar 2026 00:00:00 +0000

This study investigates the numerical simulation of nanoparticle-enhanced non-Newtonian blood flow with internal heat generation in a dilated stenotic artery using the Casson fluid framework and analyzes the effects of different parameters on flow characteristics. The research is motivated by the need to understand the joined effects of nanoparticles, magnetic fields, and thermal radiation in stenosed arteries a topic with direct implications for targeted drug delivery and hyperthermia treatment in cardiovascular diseases.

The governing mathematical model is formulated applying the Casson fluid framework and modified to an ordinary differential equations in system form and numerically solved with the application of bvp4c solver in Maple. Graphical and tabular illustrations are used to examine key flow characteristics including velocity and temperature profiles, Nusselt number and coefficient of skin friction.

The outcomes display that velocity increases with rising curvature flow parameter, stenosis height, and nanoparticle volume fraction, whereas it drops with increasing magnetic field parameter and Casson fluid parameter. Temperature increases with Casson fluid parameter, curvature parameter, stenosis height, and magnetic field strength, but decreases with nanoparticle volume fraction, Prandtl number, and thermal radiation parameter. A slight but noticeable variation is observed between alumina (Al2O3) and ferric oxide (Fe3O4) nanoparticles with respect to the volume-fraction parameter.

The study gives valuable understanding to the behavior of nanofluid fluid flow in stenosed arteries, which may guide the development of effective therapeutic and diagnostic techniques for cardiovascular diseases, particularly in selecting appropriate nanoparticles for targeted therapy. The numerical approach using bvp4c solver proves effective for analyzing complex hemodynamic phenomena.

k−type Slant Helices for Modified Orthogonal Saban Frame on \(S^2_1\) and \(H^2_0\)

Mehmet Bekta, Kubra Bulut Baykara — Wed, 11 Mar 2026 00:00:00 +0000

This article examines slant helices for modified orthogonal Saban frames on timelike and spacelike curves with geodesic curvature on \(S^2_1\) and hyperbolic curves with geodesic curvature on \(H^2_0\) . In particular, it presents statements and proofs of novel theories for k−type slant helices.

Analytical Study of Convective Heat and Mass Transfer in MHD Nanofluid Flow Over a Stretching Sheet with Thermal and Concentration Effects

Chukwuemeka Paul Amadi, Emeka Amos, Davies Iyai — Sat, 14 Mar 2026 00:00:00 +0000

The study of convective heat and mass transfer in nanofluid flow over a stretching sheet, particularly under the combined influence of thermal and concentration gradients presents meaningful structures in the field of nanofluid dynamics. This research focuses on two-dimensional magnetohydrodynamics boundary layer flow of a nanofluid over a stretching sheet in the presence of concentration-based internal heat, chemical reaction, Brownian motion and thermophoresis. The governing partial differential equation were transformed to dimensionless form using nondimensional variables and the resulting equations were solved using homotopy perturbation method. The effect of various physical parameters on velocity, temperature and nanoparticles concentration are discussed with the aid of graphs. It is observed that the increase in the Brownian motion parameter and concentration based internal heat increases the temperature distribution throughout the boundary layer. Increasing the chemical reaction significantly decreases the concentration level while increase in the magnetic field significantly reduces the fluid velocity. The results are compared with the existing literatures on various special cases to check the accuracy of the present study and are found to be in excellent agreement.

Fractional Complex Calculus and Analytic Structures on Nonlocal Complex Domains

Harlish Sharma, Anil Kumar Menaria — Sat, 14 Mar 2026 00:00:00 +0000

This work establishes a nonlocal analytic framework in the complex plane by introducing a symmetric fractional complex derivative constructed through symmetric complex increments. The proposed operator differs from classical Riemann—Liouville and Caputo derivatives and preserves rotational compatibility and phase–consistent scaling in the complex plane. Using this framework, we derive fractional analogues of Cauchy conditions, a nonlocal Cauchy—Pompeiu identity, and a fractional Liouville theorem, together with a Laurent-–Mittag-–Leffler type expansion. The analysis is developed using symmetric increment techniques and fractional contour integral representations. As a proof of concept, a fractional harmonic potential model is examined, demonstrating memory-driven deformation in analytic flows. The framework provides a mathematical foundation for fractional holomorphic geometry, memory influenced signal processing, and nonlocal complex PDE models.

Solution Properties of Transient Mixed Convection Flow in a Vertical Micro-annulus with Internal Heat Generation and Variable Viscosity Effects

K. A. Mkpedem, M. O. Durojaye — Sat, 14 Mar 2026 00:00:00 +0000

This paper examines the properties of solution of transient mixed convection flow in a vertical micro- annulus with internal heat generation and variable viscosity effects. A mathematical model describing the coupled momentum and energy equations is formulated using Boussinesq approximation and transformed into a non-dimensional form. The existence and uniqueness of the solution are established. The Kolodner–Pederson’s lemma is then employed to examine the qualitative behaviour of the solution. The study establishes that, the mathematical model is well-posed and physically consistent, the fluid velocity \(\phi\)(\(\eta,t\)) and fluid temperature \(\phi\)(\(\eta,t\))are bounded, exhibit thermal stability and evolve monotonically in a predictable manner over time toward finite limiting values. These findings contribute to the theoretical understanding of heat transfer processes in micro-scale annular systems with applications in thermal energy storage, cooling techniques, and engineering heat transfer devices.

Comparative Analysis of Parameter Estimation Methods for the Transmuted Exponential-New Weibull Pareto Model: Method of Moments, Maximum Likelihood, and Expectation–Maximization

N. O. Nweze, B. Maijama’a, C. U. Onwuamaeze, M. O. Adenomon — Thu, 19 Mar 2026 00:00:00 +0000

Flexible lifetime distributions are crucial for modeling skewed and heavy-tailed data commonly encountered in reliability, environmental studies, and risk modeling. The practical utility of these models depends on efficient parameter estimation methods that provide accurate and stable estimates, particularly for distributions with complex likelihoods. This study presents a comparative analysis of three parameter estimation methods—Method of Moments (MM), Maximum Likelihood Estimation (MLE) method, and the Expectation-Maximization (EM) algorithm for the Transmuted Exponential-New Weibull Pareto (TE-NWP) distribution. The TE-NWP extends the New Weibull Pareto distribution by introducing a transmutation parameter, enhancing flexibility in modeling skewed and heavy-tailed lifetime data. Due to its five parameters, the TE-NWP likelihood function is highly nonlinear, making analytical solutions challenging. To assess estimator performance, a Monte Carlo simulation was conducted with sample sizes of n = 20, 100, and 500, using 1,000 replications per scenario to evaluate bias and mean squared error (MSE). The results indicate that the EM algorithm consistently yields smaller bias and lower MSE than the MM and MLE methods, particularly as the sample size increases. The estimation methods were further applied to Kevlar 373/epoxy fatigue fracture data. Based on the log-likelihood, Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC), the EM-based estimates provided the best fit to the data. These findings suggest that the EM algorithm is the most efficient approach for estimating TE–NWP parameters, and thus serves as a valuable tool for analyzing complex lifetime data in reliability and risk studies.

Non-conformability of the Moment Generating Function: Rayleigh Probability Function Case

A. T. Adeniran, R. O. Olatunbosun — Mon, 23 Mar 2026 00:00:00 +0000

Non-existence has been highlighted in literature as the major limitation of the moment generating function (MGF) for some random variables (e.g. Log-Normal, Cauchy) due to divergence in their series. This study investigates (with focus on the Rayleigh probability function) the case where MGF exists but not conforming with the traditional method of deriving moments (μ′_r and or μ_r). Results show that the MGF of a Rayleigh random variable exists, uniformly continuous, infinitely differentiable, converge absolutely, and M(0) = 1, yet moments derived from MGF are in-homogeneous with the orthodox moment method.

Adaptive Grid Refinement for Enhanced Accuracy and Efficiency in One-dimensional Forward Magnetotelluric Sounding

Oladayo Emmanuel, Oduselu-Hassan, Akpabokigho Lucky Panya, Ignatius N. Njoseh — Fri, 27 Mar 2026 00:00:00 +0000

This paper introduces the one-dimensional (1D) forward solving of the magnetotelluric (MT) sounding problem through the concept of the grid adaptation approach, and it displays a numerical solution. Conventional uniform grid techniques have commonly found difficulty in both properly resolving sharp resistivity contrasts and high conductive layers and skinny conducting layers without high computational expenses. To overcome these shortcomings, a dynamic grid refinement method was proposed that focuses on grid nodes where the solution may be particularly sensitive and where the gradients of resistivity may be large. Operating the governing equations on both uniform and adaptive meshes in the finite difference discretisation scheme, the overall performance of the methods has been compared systematically. The findings illustrated that the adaptive grid refinement strategy really enhanced the accuracy of solutions, decreased computation time, and converged rapidly in comparison to the uniform grid technique. These complex, multi-layered conductivity models were easily able to be handled, and the frequency-varying skin depth was well-represented by the adaptive method throughout a wide frequency range. Variations of resistivity contrasts were also examined, whereby the adaptive grid was able to deliver significant improvements in terms of accuracy, especially in medium- and high-contrast environments. Besides, a tendency to convergence analysis and visualization using one-dimensional, two-dimensional, and three-dimensional diagrams confirmed the excellent use of the adaptive grid approach in modeling the responses of MT. The adaptive model is a computationally efficient and robust method of forward MT modelling and is best adapted to realistic geophysical situations. The further development of the approach will be directed to higher-dimensional MT issues and solving equations with real field data and inverse modelling.

Analytical Solutions on Portfolios of Investments for Stock Markets: A Laplace Transform Approach

E. Chikwem, G. L. Nwosu — Mon, 30 Mar 2026 00:00:00 +0000

This study introduces a Laplace transform approach to derive analytical solutions for investment portfolios in volatile stock markets, with a focus on the Nigerian context. Traditional models like mean-variance analysis often fail to capture stochastic dynamics, volatility, and time-dependent factors in emerging economies. By formulating systems of second-order differential equations for asset prices and applying Laplace transforms, closed-form solutions incorporating modified Bessel functions are obtained, revealing symmetric properties and normal distributions of asset values. Results from graphical analyses demonstrate how volatility influences gradual price stabilization, maturity parameters reduce short-term fluctuations, and growth rates balance risk-return dynamics. The framework provides robust tools for asset allocation, risk assessment, and forecasting, offering practical implications for investors and policymakers in navigating market uncertainties.

Global Convergence of Adaptive Momentum with Gradient Thresholding for Strongly Convex Functions

Laisin Mark, Mba Nnenna Ude, Odilichukwu Christian Okoli, Francis O. Nwawuru — Tue, 31 Mar 2026 00:00:00 +0000

This paper proposes an adaptive momentum with gradient thresholding (AMGT), a novel first-order optimization algorithm tailored for strongly convex functions. AMGT integrates adaptive momentum dynamics with a gradient thresholding mechanism to enhance convergence speed, stability, and robustness. Unlike conventional methods such as gradient descent or Adam, AMGT adaptively modifies both the momentum term and step size based on gradient magnitude and local curvature. The algorithm performs fine-grained control over updates: suppressing overshooting in early stages and allowing more aggressive steps as it nears a minimum. We provide a rigorous theoretical analysis demonstrating that AMGT achieves global convergence to the unique minimizer under standard assumptions of strong convexity and smooth differentiability. Specifically, we show that the gradient norm converges to zero and the sequence of iterates approaches the stationary point of the objective function. To validate the method, we conducted numerical experiments on several strongly convex benchmark functions, including quadratic functions, regularized least squares, and ridge regression tasks. Results show that AMGT consistently outperforms standard gradient descent, Nesterov accelerated gradient, and Adam in terms of convergence rate, stability near the minimizer, and sensitivity to step parameters. Across all experiments, AMGT achieved faster reduction in objective value and required fewer iterations to reach a specified accuracy threshold. These findings confirm that AMGT is an effective and reliable optimization framework for strongly convex problems, offering both theoretical guarantees and practical efficiency.

A Prey Predator Conservation Model for a Fishery with a Reserve Area and Prey Refuge: A Study of Lake Victoria

Silas Were Wasike — Fri, 03 Apr 2026 00:00:00 +0000

The loss of species in most fishery ecosystems worldwide has reached crisis levels driven by habitat loss, overfishing, invasive species predation and climate change. This threatens biodiversity and sustainability of these fisheries. In Lake Victoria a major decline has been observed in haplochromines due to predation by Nile perch and the species is now in danger of extinction haplochromines are important to the lake because the feed on algae preventing algal bloom. In this paper a prey-predator conservation model for a fishery with a reserve area and prey refuge has been formulated using a logistic nonlinear di erential equations. The model incorporates Holling type II functional response of the predator towards the prey. In this research we study and analyze the stability of the prey-predator dynamic system of Nile perch (predator) and haplochromines (prey) in Lake Victoria. The lake ecosystem is divided into two parts, the reserve area and unreserved area. Equilibrium points have been determined and their local and global stability established by use of eigen value approach, Bendixon-Dulac criterion and lyapunov function. The e ect of the reserve area and prey refuge on the stability of the system has been determined by simulation in MATLAB. Results show that a reserve area makes the system stable, and for certain values of migration rate 0:3 the population of the predator can coexist with prey.

Function-Space Supertopological Rings: m-Topology, d-Boundedness and Radical Structure

Bhaskar Vashishth — Thu, 16 Apr 2026 00:00:00 +0000

The theory of supertopological rings, based on D-supercontinuity, provides a natural framework for studying rings of functions that fail to be topological rings under classical continuity assumptions. In this paper we develop a detailed ring-theoretic analysis of subrings of R^X endowed with the m-topology and introduce the notion of functional generation as the fundamental structural condition governing supertopological compatibility.

We prove that a subring of R^X admits a supertopological ring structure under the m-topology if and only if it is functionally generated, thereby establishing a sharp maximality criterion. The internal algebraic structure of such rings is studied in depth: ideals and their d-closures preserve functional generation, zero divisors form d-closed sets, and d-boundedness arises naturally from the function-space setting. Lattice-theoretic properties are established, showing closure under arbitrary intersections and failure under unions

Statistical Assessment of Ambient Air Pollutants and Air Quality index in Agartala Smart City vis-à-vis Guwahati and Delhi in India

Khokan Debnath, Koushal Saha, Goutam Saha — Wed, 22 Apr 2026 00:00:00 +0000

Background: The Air Quality Index (AQI), developed by the Central Pollution Control Board (CPCB), is used to communicate overall air quality by combining multiple pollutants into a single value with defined health categories.

Aim: The present study conducted a comprehensive data-driven statistical assessment of ambient air quality parameters in Agartala Smart City, with comparative analysis of Guwahati and Delhi, representing different levels of urbanization, emission intensity, and meteorological variability.

Study Design: The study adopts a comparative and analytical research design integrating environmental chemistry with statistical methods to examine spatial and temporal variations in air pollution.

Place and Duration of Study: The study focuses on three Indian cities—Agartala, Guwahati, and Delhi. Secondary data were collected for a defined study period from official monitoring agencies.

Methodology: The research considers major air quality indicators such as PM₂.₅, PM₁₀, NO₂, and SO₂, which are key determinants of the Air Quality Index (AQI) and public health risk. Data were obtained from the Central Pollution Control Board and respective State Pollution Control Boards. A structured statistical framework was employed, including descriptive statistics, coefficient of variation, correlation analysis, and time-series-based linear trend modeling. These techniques were used to evaluate pollutant concentration patterns, variability, interrelationships, and trends across the selected cities. Comparative statistical diagnostics were applied to identify regional disparities in atmospheric pollution characteristics.

Results: Both North-Eastern (NE) cities show a sharp 2020 dip COVID-19 lockdown effect followed by rapid recovery. Delhi's AQI remains persistently 2.5× higher than Agartala's. Agartala sits above Guwahati in most years but gap is closing sharply post-2020 in PM_2.5. PM₁₀ concentrations are driven primarily by road dust, construction, and industrial emissions. Guwahati's topographic trapping is especially visible — its PM₁₀ rose 31% from 2014 to 2023.

Discussion: The findings reveal significant inter-city variation in air quality. Delhi exhibits consistently higher by 11x according to WHO standards pollutant concentrations due to intense vehicular traffic, industrial emissions, and construction activities. Guwahati shows moderate pollution levels influenced by urban expansion and meteorological conditions. Agartala, although relatively less polluted, demonstrates increasing variability in particulate matter levels due to transportation, roadside dust, biomass burning, and seasonal effects. The coefficient of variation and correlation analysis indicate strong interdependence among pollutants, suggesting common anthropogenic sources and atmospheric transformation processes.

Conclusion: The study demonstrates that statistical analysis provides valuable insights into urban air pollution dynamics and regional variability. While Agartala currently maintains relatively better air quality, the observed increasing variability in pollutant levels indicates emerging environmental concerns. The findings highlight the need for proactive, region-specific air quality management strategies and reinforce the importance of data-driven approaches for sustainable urban environmental planning and policy formulation.

Existence, Uniqueness and Solution Properties of Transient Mixed Convection Flow in A Vertical Concentric – Annulus Filled with Porous Materials Having Constant Porosity

Mkpedem K. A., Olayiwola R. O. — Mon, 27 Apr 2026 00:00:00 +0000

The existence, uniqueness, and solution characteristics of transient mixed convection flow of an incompressible viscous fluid in a vertical concentric annulus filled with a porous medium of constant porosity are investigated. Under the Boussinesq approximation, the governing momentum and energy equations incorporating buoyancy, pressure gradient, and magnetic field effects are formulated. The equations are non-dimensionalized using appropriate scaling to obtain key parameters such as Reynolds number (Re), Grashof number (Gr), Peclet number (Pe), and magnetic parameter (M). The reduced system is analyzed using similarity transformations. The existence and uniqueness of solutions are established using the Picard–Lindelöf theorem. The results confirm that the system admits a unique bounded solution, ensuring well-posedness of the model. The research shows how essential dimensionless characteristics such as Reynolds, Grashof, Peclet, and magnetic parameters affect flow and thermal behaviour. Overall, this study establishes a solid theoretical foundation for future analytical and numerical research of convection flows in porous annular geometries.

The Orbit Structure of the Product of Four Alternating Groups Acting on the Cartesian Product of Four Sets of Ordered Tuples

Moses K. Maraka, Lewis N. Nyaga — Tue, 28 Apr 2026 00:00:00 +0000

This paper explores the orbit structure of the direct product of four alternating groups acting on the Cartesian product of four sets of ordered y-tuples. The associated orbitals and suborbits lengths are determined using combinatorial formulae. Contrary to previous studies involving ordered pairs or fewer group factors, this setting introduces significantly higher combinatorial configurations arising from higher-dimensional tuple structures. This brings rise to a general orbit structure pattern that do not arise in pair-based and fewer group factors cases. The number of orbitals of A_n1 × A_n2 × A_n3 × A_n4 acting on U₁^[γ] ×U₂^[γ] ×U₃^[γ] ×U₄^[γ] , (∀ n-γ≥2) is and explicit suborbits lengths formulae are obtained using combinatorial methods. The results extend existing research on ranks and subdegrees while revealing new structural phenomena unique to actions on ordered -tuples of direct product of four alternating groups.

Stability Analysis of a Four-Dimensional Football Passing Dynamics

Tue, 05 May 2026 00:00:00 +0000

The model developed in this study is novel. A carefully structured four-dimensional football passing dynamics is formulated to analyze ball flow and possession play. The compartments: defense, midfield, forward, and goal were aggregated player roles. The model achieved analytical tractability and preserved essential and realistic directional flow of play. The study focused on the stability analysis of the model, and theoretical analysis of structured ball movement. The results of the study showed that the model remained consistent at all times. Using a constructed Lyapunov function, the study showed that under suitable conditions, the equilibrium is globally asymptotically stable. If P0 < 1, the system is stable and dominated by decay.

Robust Classification of Stock Market Volatility Using Median Absolute Deviation: Evidence from Global Indices

Sohom Majumder, Vivek Pathak — Tue, 05 May 2026 00:00:00 +0000

Aims: The aim of this study is to develop and evaluate a robust mathematical framework for stock market regime classification using the Median Absolute Deviation (MAD), and to compare its performance with conventional standard deviation-based and quantile-based classification methods under non-Gaussian financial conditions.

Study Design: Quantitative analytical study based on statistical modelling and empirical evaluation.

Place and Duration of Study: The study utilizes secondary financial data from major global equity indices, namely NIFTY 50 (India), S&P 500 (USA), and Nikkei 225 (Japan), over the period from January 2020 to January 2026.

Methodology: Daily log returns were computed from adjusted closing prices. A MAD-based standardized score was used to classify market regimes into five categories. Two benchmark methods, namely standard deviation-based and quantile-based classification, were implemented for comparison. Robustness was evaluated using Regime Balance Index (RBI), Extreme Sensitivity Score (ESS), and Label Stability Ratio (LSR) under controlled outlier contamination. Statistical validation was performed using bootstrap resampling to compute 95% confidence intervals, along with paired t-tests and Wilcoxon signed-rank tests to assess significance.

Results: The MAD-based method consistently achieved superior robustness across all datasets. For NIFTY 50, the LSR was 0.9856 compared to 0.9142 (SD-based) and 0.9738 (quantile-based). Similar improvements were observed for S&P 500 (0.9862 vs 0.8967 and 0.9750) and Nikkei 225 (0.9860 vs 0.8876 and 0.9743). The ESS was significantly lower for the MAD method (≈0.014) compared to SD-based methods (up to 0.1124). Bootstrap confidence intervals were narrow, and all statistical tests yielded p-values < 0.001, confirming the significance of the results. The findings have important implications for investors, portfolio managers, and financial analysts, as the proposed framework enables more reliable identification of market risk regimes under extreme volatility conditions.

Conclusion: The MAD-based classification framework provides a robust and statistically reliable alternative for stock market regime detection, particularly in environments characterized by extreme volatility and non-normal return distributions.

Noise Induced almost Sure Exponential Stability of a Nonlinear Delay Differential Equation with a Constant Time Lag

Donatus Ijeoma Anonwa, Augustine Omoghaghare Atonuje — Wed, 06 May 2026 00:00:00 +0000

This study investigates the effect of multiplicative white noise on stabilizing nonlinear delay differential equation which generally appear unstable in their deterministic form. The applied technique includes Lyapunov sample exponents and stochastic perturbation methods. By applying multiplicative white noise to the deterministic system, the resulting system becomes stochastically stable in an almost sure exponential sense. It demonstrates that, under certain conditions appropriate noise intensity and small delay the system achieves almost sure exponential stability.

A Unified Analytical Framework for Stability and Energy Analysis of Multi-Term Fractional Dynamical Systems

Haresh Chaudhary, Naresh Menaria — Sat, 09 May 2026 00:00:00 +0000

This work develops a unified fractional calculus framework for modeling memory dependent behavior in viscoelastic materials, electrical circuits, and control systems. The study emphasizes rigorous mathematical analysis of multi-term fractional operators and establishes well posedness and dissipativity properties for heterogeneous fractional viscoelastic models through a novel energy functional approach. For fractional order circuit representations, a bounded input bounded output stability result is derived, ensuring the physical realizability of nonlocal impedance elements. In the control domain, a practical stability theorem is proven for adaptive fractional PID controllers, providing guaranteed bounded tracking performance under memory driven adaptation. These results demonstrate that fractional operators not only enhance modeling flexibility but also preserve fundamental stability and energy principles, offering a mathematically consistent foundation for advanced engineering system design.

Triharmonic Curves on 3-Dimensional Strict Walker Manifolds

Münevver Yıldırım Yılmaz, Ayşe Dolu — Sat, 09 May 2026 00:00:00 +0000

Biharmonic curves in three-dimensional strict Walker manifolds have already attracted some attention in the literature. However the corresponding theory of triharmonic curves has not yet been addressed. The main motivation of this paper is to fill this gap by studying triharmonic curves in three-dimensional strict Walker manifolds and present explicit characterizations of triharmonic curves and their geometric properties. In this paper, triharmonic curves in three-dimensional strict Walker manifolds endowed with a Lorentzian metric are investigated. After recalling the geometric structure of strict Walker manifolds and polyharmonic curves, the triharmonic curve equation is formulated in the Lorentzian setting. Also the necessary and sufficient conditions for a curve to be triharmonic in a three-dimensional strict Walker manifold are given and such curves are characterized in terms of their curvature and torsion functions. The obtained results extend the theory of harmonic and biharmonic curves to the higher-order variational framework of triharmonic maps within the Walker Lorentzian context.

Statistical Evaluation of Digital Screen Exposure and Its Impact on Academic Performance and Behavioral Patterns: Evidence from Female Undergraduates of Maharaja Bir Bikram College

Likhmi Debatrata, Apurba Das, Nabarupa Banik, Goutam Saha — Tue, 12 May 2026 00:00:00 +0000

Background: The rapid proliferation of smartphones driven by 4G and 5G internet connectivity has significantly transformed the academic and social behavior of college students. Despite growing digital engagement, limited research in the Indian context has examined the simultaneous effects of screen exposure on academic attention and moral value formation among female undergraduates.

Objective: This study aimed to investigate smartphone usage patterns, their academic impact, and behavioral implications among female undergraduate students of Maharaja Bir Bikram College, Agartala, Tripura.

Methods: A descriptive observational cross-sectional study was conducted among 68 female undergraduate students selected through convenience sampling. A structured, closed-ended questionnaire with Likert-scale items was administered. Statistical analyses included frequency distributions, percentage analysis, and chi-square tests performed using SPSS software.

Results: A majority of respondents (55.88%) used smartphones for more than three hours daily. High proportions used smartphones for skill development (52.9%), online group discussions (52.9%), and quick feedback (73.5%). Nonetheless, 45.6% agreed smartphones distracted them from studies. Chi-square analysis revealed significant associations between year of study and attention from studies (χ² = 18.54, df = 8, p < 0.05), and between age and perceived moral impact (χ² = 16.16, df = 8, p < 0.05).

Conclusion: While smartphones serve as valuable academic tools, excessive usage adversely affects concentration and ethical development among female students. Institutions are urged to implement structured digital wellness frameworks.

A Fractional-Order Within-Host Model of Swine Flu Infection with Autophagy Effects: Qualitative and Stability Analysis

Tue, 12 May 2026 00:00:00 +0000

Swine influenza (H1N1) is a rapidly replicating respiratory virus characterized by complex within-host interactions between epithelial target cells, infected cells, and immune-mediated intracellular processes. In this study, we develop and analyze a fractional-order mathematical model describing the within-host dynamics of H1N1 infection, explicitly incorporating autophagy as a key intracellular antiviral mechanism. The model is formulated using Caputo fractional derivatives to account for memory effects associated with delayed viral replication, immune activation, and persistence of infection observed in influenza pathogenesis. We establish fundamental qualitative properties of the model, including positivity, boundedness, and the existence of a biologically feasible invariant region. The disease-free equilibrium and was derived, and the basic reproduction number R0 is obtained using the next-generation matrix. This represents the threshold for viral establishment within the host. The stability analysis conducted showed that the infection was cleared when R0 < 1. Sustained viral replication occurs when R0 > 1, consistent with known influenza infection behavior. The results of the study demonstrates that autophagy does not influence the initial infection threshold. It although reduces viral load significantly and impede infected cell burden during the progression phase of H1N1 infection. The fractional-order model analysis further reveals that memory effects slow down infection dynamics. This reflects clinically observed delays in viral peak and immune response activation. The findings of this study provides a more realistic mathematical representation of swine flu infection kinetics. It also highlights the potential of targeting autophagy pathways as a therapeutic strategy for controlling influenza severity.

A Comprehensive Benchmarking of Classical Conjugate Gradient Methods under Strong Wolfe Line Search Conditions

Michael Oluwaseun Ayansiji — Tue, 12 May 2026 00:00:00 +0000

The Strong Wolfe line search conditions are widely recognized for providing robust theoretical convergence guarantees in nonlinear conjugate gradient (CG) methods, yet their practical efficacy compared to simpler inexact line searches remains underexplored for large-scale optimization. This study presents a comprehensive numerical evaluation of eight classical CG methods, BAN, FR, PRP, HS, CD, DY, LS, and HZ, under the Strong Wolfe line search framework. Through extensive experiments on 50 high-dimensional benchmark problems (n = 5,000 and 10,000) from the CUTEr collection, we assess convergence rates, computational efficiency, and robustness using rigorous statistical analysis. Results indicate that the Polak–Ribière–Polyak (PRP) method achieves the highest success rate (88%) and statistical dominance, followed by Liu–Storey (LS) at 78% and Hager–Zhang (HZ) at 70%. A novel comparative analysis with prior Armijo-based findings reveals that Strong Wolfe improves stability for methods like HS and DY but introduces computational overhead that erodes performance gains for LS and HZ. Statistical significance testing (Wilcoxon signed-rank, α=0.05) confirms PRP's superiority over all other methods under Strong Wolfe conditions. However, Strong Wolfe introduces 12–38% computational overhead compared to Armijo, highlighting a trade-off between convergence reliability and efficiency. This work provides the first comprehensive benchmarking of classical CG methods under uniform Strong Wolfe conditions, offering actionable insights and a decision framework for practitioners in selecting appropriate line search strategies for large-scale unconstrained optimization problems.

Implementation of Shifted Vieta-Lucas Polynomials via Collocation for the Numerical Assessment of Volterra Integro-Differential Equations

Otaide Ikechukwu Jackson, Okwonu Friday Zinzendoff — Wed, 13 May 2026 00:00:00 +0000

This study introduces a robust numerical method that combines shifted Vieta-Lucas polynomials, the variational iteration approach (VIA), and collocation method (CM) to efficiently solve Volterra integro-differential equations. The method transforms the given equation into a solvable algebraic system by leveraging the orthogonal properties of shifted Vieta-Lucas polynomials as trial functions. Convergence is rigorously established via Banach's fixed-point theorem, confirming that the iterative scheme yields a unique, convergent Cauchy sequence. Validation on Linear second and third order problems demonstrates superior accuracy and faster convergence compared to traditional Legendre collocation methods, with absolute errors significantly reduced even at low polynomial degrees. Graphical results further confirm strong agreement with exact solutions, positioning the proposed technique as a powerful and mathematically sound alternative for integro-differential equations. All computations were done using Maple 18.

Generalized Lattice Isomorphisms in Modules over Non-commutative Rational Function Rings with Applications to Multidimensional Dynamical Systems

Fri, 05 Jun 2026 00:00:00 +0000

The paper discusses the restriction of the theory of classical lattice isomorphism to the analysis of algebraic systems, in which current results are mostly restricted to modules over rings of polynomials and therefore to the analysis of causal systems. The main omission is that there is no single framework which can manage modules across rational function rings, and these are required to model noncausal, multidimensional, and distributed dynamical systems. In order to fill this gap, the paper constructs a lattice-theoretic generalised framework of finitely generated modules over the rings of rational functions in terms of module theory, localisation and bilinear forms. It is a combination of structural analysis of submodules, annihilator theory and duality by non-degenerate bilinear mappings to generalise classical results. The principal finding is that, given a non-degeneracy condition, there is a lattice isomorphism (up to duality) between the lattice of submodules of a module over a rational function ring and the submodule lattice of its annihilator. This theorem is a generalisation of the classical lattice isomorphism by Fuhrmann between polynomials and rationals, with all the necessary lattice operations maintained but allowing a more arbitrary algebraic structure. It has been extended to multidimensional dynamical systems, in which it allows the study of noncausal and spatially distributed phenomena. Control theory, coding theory and signal processing have practical implications where rational representations give a better model of the interconnections of complex systems and system structure.

A Comprehensive Review of Fuzzy Logic and Stochastic Methods for Environmental Risk and Pollution Modelling

Thu, 12 Mar 2026 00:00:00 +0000

Environmental systems are inherently complex and uncertain, influenced by numerous interacting factors including weather variability, pollutant emissions, and human activities. Traditional deterministic modelling approaches often fail to capture both the random variability of these systems and the imprecision inherent in expert knowledge. This paper presents a comprehensive review and application of hybrid fuzzy–stochastic modelling techniques for environmental risk assessment and pollution prediction. Fuzzy logic provides a framework to incorporate qualitative and linguistic information, allowing expert judgments and regulatory standards to be expressed in interpretable terms such as “high risk” or “moderate contamination.” Stochastic mathematics captures random variations in environmental variables, representing uncertainty through probability distributions, simulations, and scenario analysis. The integration of these approaches enables dual representation of uncertainty, combining probabilistic risk assessment with qualitative reasoning, which enhances predictive accuracy and supports informed decision-making. The paper discusses practical applications across air and water pollution management, soil contamination, and climate-related risk assessment, highlighting the value of hybrid models in situations with incomplete data or high variability. Advancements in adaptive fuzzy rule-based systems, high-resolution stochastic simulations, and data-driven calibration techniques are examined, demonstrating how these innovations improve the responsiveness, flexibility, and interpretability of environmental models. Case studies illustrate the effectiveness of hybrid models in predicting urban air quality, contaminant transport in water bodies, and the impact of extreme environmental events. Finally, the paper identifies future research directions, including integration with real-time sensor data, multi-scale modelling, artificial intelligence optimisation, and enhanced visualisation techniques. Overall, the hybrid fuzzy–stochastic framework offers a robust and versatile tool for sustainable environmental management, providing decision-makers with comprehensive, interpretable, and actionable insights into complex environmental risks. The approach facilitates both immediate operational decisions and long-term planning, supporting the development of resilient, adaptive, and scientifically informed environmental policies.

Deep Learning and PDE-Based Models for Geological Hazard Prediction

Mon, 06 Apr 2026 00:00:00 +0000

Geological hazards including landslides, earthquakes, volcanic eruptions, and floods—pose significant risks to human societies, infrastructure, and ecosystems. Reliable prediction and risk assessment are essential for effective disaster mitigation and resilience planning. Conventional approaches, such as empirical methods and physics-based simulations, often face limitations in capturing the complex, nonlinear, and multi-scale behavior of geological systems. Recent advances in deep learning and partial differential equation (PDE)-based modeling offer promising alternatives to address these challenges.

Deep learning techniques, including convolutional neural networks (CNNs) and recurrent neural networks (RNNs), can extract complex spatial and temporal patterns from large-scale datasets such as seismic records, satellite imagery, and in situ sensor measurements. In parallel, PDE-based models provide physics-informed representations of geological processes by describing system evolution under governing physical laws and boundary conditions. Integrating these methodologies has led to hybrid frameworks, such as physics-informed neural networks (PINNs) and coupled PDE–deep learning models, which combine data-driven adaptability with physical consistency and improved generalization.

This review summarizes state-of-the-art applications in landslide susceptibility mapping, seismic hazard assessment, and flood prediction. It also discusses key challenges, including data quality and heterogeneity, model transferability across regions, uncertainty quantification, and computational demands. Case studies demonstrate that integrated modeling approaches enhance predictive accuracy and support real-time early warning systems. Future research directions include multi-hazard modeling, integration with Internet of Things (IoT) sensor networks, and scalable real-time monitoring frameworks to advance predictive geoscience and disaster resilience.

Graph Theory and Computational Approaches in Ecosystem Interaction Networks

Wed, 25 Feb 2026 00:00:00 +0000

Ecosystems are inherently complex, consisting of multiple interacting species, environmental factors, and anthropogenic influences. Understanding these interactions is crucial for predicting ecosystem stability, resilience, and responses to environmental changes. This paper explores the application of graph theory and computational modelling to analyse and quantify interactions within ecological networks. Graph theory provides a framework to represent species and their interactions as nodes and edges, enabling the identification of key species, trophic structures, and functional modules. Computational approaches, including network analysis algorithms, simulations, and modelling of dynamic processes, allow researchers to study the propagation of perturbations, the emergence of stability, and the impact of environmental stressors. Hybrid methods combining graph-theoretic metrics with probabilistic and stochastic models further enhance the prediction of ecosystem responses under uncertainty. Case studies demonstrate the effectiveness of these approaches in assessing food web stability, predicting species extinction cascades, and understanding spatial–temporal patterns of biodiversity. The paper also discusses challenges such as data incompleteness, uncertainty in interactions, and the computational complexity of large-scale networks. Future directions include integrating multi-layered networks, machine learning for pattern recognition, and real-time monitoring using sensor networks. Overall, the integration of graph theory with computational techniques provides a robust and versatile framework for ecosystem analysis, supporting conservation planning, sustainable resource management, and ecological risk assessment.

AI-Driven Biodiversity Conservation: Integrating Evolutionary Game Theory, Environmental Data, and Multi-Agent Modelling

Parsanta, Ravi Kumar, Avni S. Thakkar, Mohammed Zubairuddin, A. Durai Ganesh — Sat, 28 Feb 2026 00:00:00 +0000

Biodiversity conservation is a pressing global challenge, as ecosystems face increasing threats from habitat loss, climate change, and human activity. Traditional conservation strategies often rely on limited field observations and heuristic approaches, which may not fully capture the dynamic interactions among species, environmental factors, and human interventions. Artificial intelligence (AI) offers advanced computational tools to analyse large-scale environmental data, uncover patterns, and optimise conservation strategies. When combined with Evolutionary Game Theory (EGT), AI provides a powerful framework to model species interactions, competition, cooperation, and resource allocation, enabling predictions of ecosystem dynamics under varying scenarios. This paper explores AI-driven biodiversity conservation strategies that integrate EGT with environmental datasets, including climate variables, land-use patterns, and species occurrence records. By leveraging machine learning models, such as reinforcement learning, neural networks, and optimisation algorithms, in combination with evolutionary game frameworks, conservation policies can be designed that promote sustainable species interactions, habitat preservation, and resilience against environmental changes. Case studies demonstrate how AI-EGT models can identify critical habitats, predict species population trajectories, and guide adaptive management practices. The results suggest that integrating AI with evolutionary game theory enhances decision-making capabilities, supports real-time monitoring, and facilitates proactive conservation measures. This approach also highlights the potential for multi-agent simulations, scenario analysis, and dynamic policy evaluation to improve biodiversity outcomes. The convergence of AI, EGT, and environmental data represents a promising frontier in ecological research, offering quantitative, data-driven solutions to complex conservation challenges.

Mathematical Modelling and Machine Learning for Geological and Ecological System Dynamics

Sat, 21 Mar 2026 00:00:00 +0000

Geological and ecological systems exhibit complex, nonlinear, and dynamic behaviour driven by interactions among physical, biological, and anthropogenic factors. Understanding these systems is critical for sustainable resource management, disaster risk mitigation, and biodiversity conservation. Mathematical modelling provides a quantitative framework to capture system dynamics, identify underlying mechanisms, and predict future behaviour under varying conditions. Machine learning (ML) offers complementary tools to process large-scale, heterogeneous datasets, detect patterns, and improve predictive accuracy. This paper aims to explores the integration of mathematical modelling and machine learning for the analysis of geological and ecological system dynamics. The combined approach enables the development of hybrid models that leverage the interpretability of differential equations, agent-based models, and network analysis with the flexibility and scalability of machine learning algorithms. Applications include landslide and flood risk prediction, species population dynamics, habitat connectivity modelling, and ecosystem service assessment. By combining domain knowledge with data-driven insights, these approaches enhance decision-making for environmental management, policy formulation, and sustainable development. Case studies demonstrate the effectiveness of hybrid models in capturing nonlinear interactions, predicting extreme events, and optimising intervention strategies. The results indicate that integrating mathematical and machine learning models provides a robust framework for understanding and managing complex geological and ecological systems, offering both theoretical insight and practical applicability in diverse environmental contexts.