Asian Research Journal of Mathematics

Structural Properties of Zero-Divisor Graphs of Multilocal Finite Rings

Presley Kiplagat — 2026-07-28

Let

\[
N=\prod_{i=1}^t p_i^{n_i}, \quad t \geq 2
\]

where the primes \(p_1, \ldots, p_t\) are distinct and \(n_i \geq 1\), and let \(R=\mathbb{Z} / N \mathbb{Z}\). The nonzero zero-divisors of \(R\) are partitioned by their truncated prime-adic valuation vectors. This paper develops the resulting valuation-layer description of the zero-divisor graph \(\Gamma(R)\). A complete formula is obtained for the size of every valuation layer, including layers containing elements that vanish in one or more Chinese-remainder components. Adjacency is shown to depend only on coordinatewise sums of valuation vectors, and the graph is therefore a blow-up of a finite weighted layer graph. This representation yields a direct proof that \(\operatorname{diam} \Gamma(R)=3\) whenever \(t \geq 2\), together with a criterion distinguishing vertex pairs at distances one, two, and three. The clique number is expressed exactly as a weighted clique optimization problem on the layer graph. In addition, independent permutations within each valuation layer are shown to form a canonical direct-product subgroup of \(\operatorname{Aut}(\Gamma(R))\); no assertion is made that this subgroup is always the full automorphism group. A complete calculation for \(\mathbb{Z} / 12 \mathbb{Z}\) illustrates the layer sizes, adjacency pattern, diameter, clique number, and canonical automorphism subgroup.

A Comparative Evaluation of Three-Class Diabetes Classification Using Machine Learning Algorithms

Ayeni Taiwo Michael — 2026-07-29

Background: Early detection of diabetes and prediabetes is important for reducing long-term complications.

Aim: This study comparatively evaluated four machine learning algorithms for three-class diabetes classification using routinely available clinical indicators from the National Health and Nutrition Examination Survey.

Methods: The analytical sample included 2,029 participants classified as normal (62.0%), prediabetic (26.7%), or diabetic (11.3%). Recursive Feature Elimination with 10-fold cross-validation was used to select predictors from 27 candidate variables. Six features were retained: fasting glucose, age, diabetes history, insulin level, waist circumference, and systolic blood pressure. Multinomial Logistic Regression, Decision Trees, Random Forest, and XGBoost were trained using a 70/30 stratified train-test split and evaluated using accuracy, Cohen’s Kappa, and class-specific performance metrics.

Results: Random Forest achieved the highest overall test performance, with 78.1% accuracy and a Cohen’s Kappa of 0.471. XGBoost, Multinomial Logistic Regression, and Decision Trees achieved accuracies of 72.6%, 73.0%, and 72.4%, respectively. All models showed high specificity for diabetes detection, exceeding 97%. Prediabetes classification remained difficult across algorithms, with sensitivity ranging from 38% to 42%.

Conclusion: Random Forest provided the best overall performance for three-class diabetes classification in this analytical sample. However, modest agreement, low prediabetes sensitivity, potential label leakage from fasting glucose, and the absence of external validation indicate that further evaluation is required before clinical application.

On Minimal R − I−open Sets and Continuous Functions in Ideal Topological Space

M. V. Sangeetha — 2026-07-31

Aims/Objectives: This paper introduces novel classes of sets and continuous functions in ideal topological spaces by incorporating the concepts of minimal open sets and R −I−open sets. These newly defined classes provide a broader framework for studying continuity and topological structures in ideal spaces. Furthermore, the paper defines and characterizes the R−I −Tmin and R−I −Tmax spaces, establishing their fundamental properties and examining their behavior. The relationships between these newly introduced continuous functions and several existing classes of continuous functions available in the literature are also investigated, highlighting similarities, distinctions, and generalizations.

Study Design: Theoretical.

Place and Duration of Study: Department of Mathematics, St. Joseph’s College (Autonomous) Devagiri, Calicut-673008, India.

Methodology: The application of logical reasoning to deduce new theorems from established principles.

Conclusion: This paper proposed a class of sets and continuous functions in R − I−space called minimal R − I−open sets and minimal R − I−continuous functions. A small discussion on minimal R − I−open sets, minimal R − I−continuous functions, and minimal R − I−open sets, minimal R − I−continuous functions is given. The relation between these continuous functions and some continuous functions that are already in literature is studied. Also, this paper surveyed R − I − Tmin and R − I − Tmax spaces and obtained that R − I − Tmin (resp. R − I − Tmax) and R − I − Ti i = 0, 1, 2 spaces are independent of each other. Similarly, R−I−Tmin (resp. R−I−Tmax) and R−I−door spaces are independent of each other.

Constructing Equienergetic Graphs Using Windmill Graph

R. V. Rajalekshmi — 2026-07-31

This study develops constructions of equienergetic graphs from a windmill graph and selected Cartesian products. Graph energy is taken as the sum of the absolute values of the adjacency eigenvalues, and two non-isomorphic graphs are equienergetic when these sums coincide. For the windmill graph W(3, n), formed from n copies of K₃ sharing a common vertex, the graph obtained by joining vertices whose distance in W(3, n) is exactly two is analysed. The common vertex becomes isolated, while the remaining vertices induce the complete n-partite graph K_2,2,...,2. Its adjacency spectrum, together with the isolated vertex, is {(2n − 2)₁, (−2)ⁿ⁻¹, 0ⁿ⁺¹}, yielding energy 4(n− 1). Since K_2n−1 has spectrum {(2n − 2)¹, (−1)²ⁿ⁻²} and the same energy, the two graphs are equienergetic. The manuscript also records that the energy of the shadow graph S(G) is twice the energy of G and uses the energies of complete and star graphs to identify another equienergetic family. Finally, Cartesian-product examples are considered. The spectrum of C₃&K₂ gives energy 8, equal to that of K₅; corresponding calculations give energies 12 and 16 for C₄&K₂ and C₆&K₂, matching K₇ and K₉, respectively. These constructions illustrate how spectral decomposition can be used to obtain explicit equienergetic graph pairs.

Variable-Viscosity Natural Convection and Heat Transfer of Diesel Fuel in Cylindrical Storage Tanks

Edwin Ooko — 2026-07-31

Aims: To investigate how temperature-dependent (Arrhenius) viscosity affects buoyancy-driven natural convection and heat transfer of diesel fuel in cylindrical storage geometries, and how this, in turn, shapes derived quantities such as the Reynolds number and pumping power. The work addresses the limitations of classical constant-viscosity models, which may misestimate flow resistance, wall shear stress, heat-transfer rate, and pumping power when the stored fuel is thermally non-uniform.

Study Design: Theoretical and numerical (computational) study.

Methodology: An Arrhenius viscosity law is embedded in the complete natural-convection governing equations: continuity; momentum with Boussinesq buoyancy and the temperature-dependent viscosity retained inside the diffusion term; and energy with thermal conduction and viscous dissipation. A similarity transformation reduces the coupled nonlinear partial differential equations to two ordinary differential equations for the dimensionless stream function f(η) and temperature θ(η), governed by the Grashof number Gr, Prandtl number Pr, viscosity parameter λ, and Eckert number Ec. The reduced system is solved by a fourth-order Runge-Kutta scheme with a secant-based shooting technique to a tolerance of 10⁻⁶. The Reynolds number is treated as a derived diagnostic rather than a primary governing variable. The model is not validated against experimental measurements; the findings should be read within the stated assumptions.

Results: Over 5-35°C, the diesel viscosity falls from about 3.5 to 0.95 mPa·s (a factor of roughly 3.7). A reference Reynolds number rises by the same factor (from about 1000 to about 3700), crossing the laminar-transitional value (Re ≈ 2300) near 25°C. The natural-convection velocity profile rises from zero at the wall to an internal peak and decays to the quiescent far field; warmer fuel (higher effective Grashof number and lower viscosity) produces a thinner, faster boundary layer. Higher Prandtl numbers and viscosity parameters thin the thermal boundary layer and raise the wall temperature gradient −θ′(0), which is proportional to the local Nusselt number. The pumping power falls to about 27% of its 5°C value at 35°C.

Conclusion: Incorporating temperature-dependent viscosity materially changes the predicted natural-convection flow and heat transfer relative to constant-viscosity models. The findings are model-based and require experimental validation before strong engineering recommendations can be made.

A Linear Ordinary Differential Equation Model of Assets and Loan Liquidity Management of Credit Unions: A Two-state Dynamic Model

Cynthia Ama Mensah — 2026-08-01

This study proposes a closed-system linear ordinary differential equation (ODE) model to analyse and predict the dynamics of liquid assets and outstanding loans in credit union liquidity risk management. Using 40 quarterly observations (2015–2024) obtained from the Central Finance Facility (CFF) of the Ghana Co-operative Credit Unions Association (CUA), the study formulates a two-state deterministic model governed by the asset-to-loan transition rate α, the loan-to-asset recovery rate β, and the loan default rate δ. Closed-form solutions are derived using the Laplace transform technique, and discrete quarterly prediction equations are obtained using a first-order Taylor expansion. Stability analysis confirms that the system is asymptotically stable when α, β, and δ are positive. Model performance is evaluated using root mean square error (RMSE), mean absolute percentage error (MAPE), and the Scatter Index (SI). The optimal asset prediction model corresponds to α = 0.0869 (MAPE = 14.27%), and the optimal loan model to ω = 0.91 (RMSE = 225,548.63). Additionally, three machine-learning models—Support Vector Regression (SVR), XGBoost, and Random Forest—are employed to generate eight-quarter-ahead forecasts (2025–2026). SVR achieves the best out-of-sample performance for forecasting both assets (MAPE = 2.92%) and loans (MAPE = 3.70%). The study concludes that the ODE-based closed liquidity model provides an analytically rigorous and practically interpretable framework for credit union liquidity planning, and that SVR-based forecasting offers a useful complement for short-term projections.

Hydrodynamic Modelling of Mixing Efficiency and Optimal Bio-methane Production in Anaerobic Digesters Using a Two-Dimensional Navier–Stokes Framework

Ruth Akumu Obande — 2026-08-03

Background: Anaerobic digestion (AD) is a proven technology for renewable bio-methane production, but digester efficiency is often limited by poor hydrodynamic mixing rather than by microbial kinetics alone; most existing models, however, assume idealised, fully homogeneous reactors.

Objective: This study investigates the influence of hydrodynamics on mixing efficiency and bio-methane production potential in anaerobic digesters using mathematical modelling.

Methods: A two-dimensional incompressible Navier–Stokes model was coupled with a tracer advection–diffusion equation to simulate slurry flow and mixing behaviour. The governing equations were non-dimensionalised using the Reynolds and Péclet numbers, discretised using the finite difference method, and solved numerically in MATLAB. An optimisation framework that treated inlet velocity as the control variable, together with an adjoint sensitivity analysis, was used to evaluate and improve mixing efficiency.

Results: At a Reynolds number of 2100, the flow exhibited transitional characteristics, with a dead zone fraction of approximately 35.1%. Velocity contours revealed limited circulation, whereas the tracer distribution showed a non-uniform concentration pattern across the domain. The dead zone fraction declined exponentially as Re increased, with values above 4000 projected to reduce it below 15%. At Pe = 10,000, transport was strongly advection-dominated, and the adjoint sensitivity analysis identified the inlet/impeller region as offering the greatest leverage over mixing performance.

Conclusion: Hydrodynamic conditions play a critical role in determining mixing efficiency and, consequently, bio-methane production potential. The developed model provides a computationally efficient framework for analysing and optimising anaerobic digester performance and offers a foundation for future integration with biochemical reaction models.

A Gravity–Poisson Framework for Synthetic Origin–Destination Demand Estimation on the Nairobi CBD–Ongata Rongai–Kiserian Public Transport Corridor

George M. Mocheche — 2026-08-03

Reliable Origin–Destination (OD) demand information is fundamental to transport planning, fleet scheduling, infrastructure investment, and policy formulation. However, in many developing cities, particularly those dominated by informal paratransit systems, comprehensive passenger-movement data are often unavailable, making conventional demand estimation difficult. This study developed and validated an integrated Gravity–Poisson framework for the synthetic estimation of passenger demand along the Nairobi CBD–Ongata Rongai–Kiserian public transport corridor, a major commuter route characterised by severe data limitations and highly directional travel patterns.

The framework combines a doubly constrained gravity model for OD trip distribution with a Poisson stochastic process for modelling passenger arrivals. Spatial interactions were estimated using demographic and geospatial proxy variables derived from population distributions and network distances, while model calibration was achieved through parameter optimisation and the Iterative Proportional Fitting Procedure (IPFP). Theoretical properties of the framework, including the existence and uniqueness of balanced OD solutions, positivity of passenger flows, trip conservation, convergence of the balancing algorithm, distance elasticity, and parameter identifiability, were formally established. Model performance was evaluated using mean absolute error (MAE), root mean square error (RMSE), sensitivity analysis, and benchmarking against XGBoost and Long Short-Term Memory (LSTM) machine-learning models.

The results revealed a highly concentrated morning commuter flow towards the Nairobi CBD, with approximately 97% of corridor demand converging at the Railways terminal. Calibration yielded a distance-decay parameter of β = 0.1000, indicating relatively weak sensitivity of commuter demand to travel distance. The balanced OD matrix satisfied all theoretical conservation and positivity conditions, while the Poisson arrival model indicated that rainfall, holidays, demonstrations, and network disruptions reduced passenger arrivals. Model calibration substantially improved predictive accuracy, and the sensitivity analysis supported the robustness of the framework under varying operational conditions.

The study demonstrates that reliable and operationally meaningful transport-demand information can be generated even in environments where conventional OD survey data are unavailable. Beyond providing a practical decision-support tool for public transport planning and fleet allocation, the framework contributes to the theoretical foundations of synthetic demand estimation by integrating spatial interaction theory and stochastic arrival modelling within a mathematically rigorous and computationally validated framework. The approach offers a scalable methodology for transport-demand analysis and mobility planning in rapidly urbanising, data-constrained regions.

Navier-stokes Based Modelling of Airflows in Forest Canopies and Its Influence on Local Climate Dynamics

Ruto Faith Chemwetich — 2026-08-05

Background: Forest canopies strongly influence atmospheric airflow, turbulence generation, heat exchange, water transport, and carbon dioxide distribution, thereby regulating the local climate. However, accurately representing airflow dynamics within forests remains challenging because of vegetation drag and turbulent mixing.

Aims: This study developed a mathematical model based on the Navier–Stokes equations to investigate airflow behaviour within forest canopies and assess its influence on local climate dynamics.

Study Design: This was a computational fluid dynamics (CFD)-based modelling study employing the Reynolds-averaged Navier–Stokes (RANS) equations coupled with the standard k–ε turbulence model.

Place and Duration of Study: Department of Mathematics and Computer Science, University of Eldoret, Kenya, between July 2025 and April 2026.

Methodology: The incompressible Navier–Stokes equations were used to model airflow within and above forest canopies. Vegetation effects were represented using a canopy drag-force term based on leaf area density. Turbulence was simulated using the standard k–ε model, while additional transport equations described temperature, water vapour, and carbon dioxide dynamics. The governing equations were discretised using the Finite Volume Method (FVM) and solved numerically in MATLAB. Simulations were performed for dense, medium, and sparse canopy configurations over a 30 m computational domain.

Results: Airflow velocity increased with height in all canopy configurations, with dense canopies showing the greatest attenuation. At canopy height, velocities were approximately 1.45 m/s, 1.95 m/s, and 2.65 m/s for dense, medium, and sparse canopies, respectively. Turbulent kinetic energy (TKE) peaked near the canopy top, reaching approximately 66 m²/s², 44 m²/s², and 22 m²/s², respectively. Temperature increased with height, while moisture and carbon dioxide concentrations decreased because of enhanced turbulent mixing. Dense canopies retained higher moisture and carbon dioxide levels than medium and sparse canopies.

Conclusion: Forest canopy density significantly influenced airflow structure, turbulence production, and scalar transport. Dense canopies provided stronger microclimatic regulation through enhanced momentum attenuation, moisture retention, and carbon storage. The developed modelling framework provides a useful tool for studying canopy–atmosphere interactions and local climate dynamics.

Queuing Generative AI Workloads with Variable Job Sizes and Memory Constraints

Payal Goswami — 2026-08-10

Generative AI inference presents a scheduling problem that differs from conventional compute workloads because requests vary substantially in service time and their memory requirements increase dynamically during autoregressive decoding. This study formulates generative AI serving as a memory-constrained, variable-size batch queue and develops a modified Pollaczek–Khinchine waiting-time approximation that includes a memory-contention penalty. It also proposes Memory-Aware Adaptive Batching (MAAB), an online admission-control policy that admits requests only when a probabilistic memory-headroom constraint is satisfied. MAAB combines projected peak memory demand with a size-aware priority score and an ageing mechanism to limit starvation. The framework was evaluated using discrete-event simulation with Poisson arrivals, shifted log-normal output lengths, and accelerator memory provisioned for heterogeneous request sizes. Four policies were compared: first-come-first-served, shortest-job-first, static batching, and MAAB. Across 50,000 completed requests and 20 replications, MAAB achieved a mean waiting time of 5.8 s, a 95th-percentile waiting time of 14.2 s, memory utilisation of 88.7%, three out-of-memory retries, and throughput of 58.6 jobs per minute. Relative to first-come-first-served scheduling, MAAB reduced mean waiting time by up to 68%, reduced out-of-memory-triggered retries by more than 95%, and increased throughput by 58%. These results support memory-aware, size-adaptive queueing as a practical approach to improving latency, utilisation, and memory safety in generative AI serving.

Mathematical Modelling of Typhoid Fever Transmission Dynamics Incorporating Antibiotic Resistance

Vincent Kyunguti Mwanthi — 2026-08-10

Typhoid fever remains a significant public health challenge, particularly in developing countries with inadequate sanitation infrastructure. The emergence and spread of drug-resistant typhoid fever strains have complicated treatment, leading to prolonged illness, higher healthcare costs, and sustained transmission within communities. This growing resistance underscores the need for effective treatment approaches and disease control strategies. This study develops a mathematical model of typhoid fever transmission that incorporates antibiotic resistance. The model categorises infected individuals into drug-sensitive and drug-resistant typhoid fever strains. The impact of treatment modification through different therapeutic options is examined to assess its effect on the prevalence of both sensitive and resistant strains. The model is analysed qualitatively, and the basic reproduction number, R₀ , is derived as the sum of two reproduction numbers, R₀^s and R^r₀, representing the transmission contributions of the sensitive and resistant strains, respectively. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined. Sensitivity analysis is conducted to identify the key parameters that influence typhoid fever transmission and persistence. Numerical simulations were performed to validate the analytical results, which demonstrated that typhoid vaccination, the use of appropriate treatment adjustment using first-line and second-line antibiotics, and improved hygiene and sanitation practices significantly reduce the prevalence of both drug-sensitive and drug-resistant strains, as well as the overall infection burden. These findings highlight the effectiveness of integrated prevention and treatment strategies in mitigating antibiotic resistance and enhancing typhoid fever control in the community

Research on Green Water Demand Prediction and Intelligent Irrigation Based on Machine Learning

Yi Han — 2026-08-11

China’s agriculture is currently in a critical phase of transitioning from traditional irrigation to intelligent, efficient, and green agriculture. Faced with the dual pressures of water resource scarcity and food security, developing smart irrigation is an important direction for promoting sustainable agricultural development. This study takes the major wheat-producing areas in Henan Province as the research object and constructs an intelligent irrigation research framework encompassing water demand prediction, feature extraction, multimodel comparison, and multi-objective optimization. First, a sliding window method is employed to construct the prediction dataset, and random forest is used to screen out 10 key meteorological variables including sunshine duration and precipitation. The water demand prediction performance of Random Forest (RF), Convolutional Neural Network (CNN), Support Vector Regression (SVR), and Long Short-Term Memory (LSTM) networks is compared, with model parameters optimized using the Sparrow Search Algorithm (SSA). Results show that the SSA-RF model achieves the best prediction performance. The SHAP method is applied to analyze feature contributions, revealing that precipitation is the main influencing factor of water demand. Predictions indicate higher water demand during the seedling stage and regreening stage of wheat. Furthermore, the NSGA-II multi-objective optimization algorithm is adopted, comprehensively considering irrigation cost, evaporation loss, and precipitation. It determines that sprinkler irrigation is optimal for the regreening, jointing, and grain-filling stages of wheat, while UAV irrigation is optimal for the seedling stage. Three scenarios conventional development, water-saving optimization, and green high-efficiency are set up, and differentiated irrigation water use strategies are proposed.

Existence and Uniqueness of Cholera Model with Vaccination

Metet K. Nelson — 2026-08-12

This study investigates the existence and uniqueness of solutions for a fractional-order cholera transmission model incorporating vaccination. The model divides the human population into susceptible, vaccinated, infected, and recovered classes, while also considering human-associated vibrios and environmental vibrios as pathogen-related compartments. The classical integer-order model is first formulated using assumptions on recruitment, indirect environmental transmission, vaccination, recovery, loss of immunity, and pathogen dynamics. The model is then extended using the Caputo–Fabrizio fractional derivative to represent memory effects in cholera transmission dynamics. Basic concepts of fractional derivatives, fractional integrals, and fixed-point theory are introduced as the mathematical foundation for the analysis. The Caputo–Fabrizio model is converted into an equivalent Volterra-type integral formulation, and the vector field associated with the model is examined for Lipschitz continuity. Under suitable boundedness and contraction conditions, fixedpoint arguments are used to support the existence and uniqueness of solutions for the proposed fractional initial-value problem. The analysis provides a theoretical basis for studying cholera dynamics with vaccination