Indexing

Abstract: Accurate prediction of pollutant transport is the foundation on which any inverse source-identification scheme is built, yet most river-pollution studies assume constant or, at most, spatially varying flow parameters and so cannot represent the unsteady conditions of natural rivers. This paper develops, derives, and validates a forward transport model based on the advection–diffusion equation (ADE) with temporally varying velocity and dispersion coefficients, in both one and two spatial dimensions. The ADE is derived from first principles through conservation of mass and the divergence theorem. For the one-dimensional case, a closed-form analytical solution is obtained by a sequence of variable transformations that reduce the variable-coefficient ADE to a constant-coefficient diffusion equation solved by Laplace transforms; a numerical solution is constructed using the Forward Time Central Space Centered Scheme (FTCSCS), whose von Neumann stability condition is derived explicitly. For the two-dimensional case, an unconditionally stable, second-order Alternating Direction Implicit (ADI) scheme is developed, with the governing equation split into an x-sweep and a y-sweep, each reduced to a tridiagonal system solved by the Thomas algorithm. The analytical and numerical 1D solutions agree closely, with RMSE decreasing from 0.028 at Pe ≪ 1 to 0.004 at Pe ≫ 1. Simulations reveal that pollutant concentration is highest near the source and decays downstream; that concentration grows with time at any fixed point; and that the longitudinal distribution becomes increasingly advection-skewed as the Peclet number rises. The effect of four temporal coefficient regimes is quantified, showing that concentration is lowest when both dispersion and velocity increase with time and highest when dispersion increases in a decelerating flow. The framework provides a physically faithful, computationally efficient forward solver suitable for generating the concentration fields required by inverse source-identification methods.

Keywords: Advection–diffusion equation; Temporally varying coefficients; Alternating direction implicit method; Laplace transform; von Neumann stability; Pollutant transport.

Title: Forward Modelling of River Pollutant Transport: Analytical and Numerical Solutions of the Advection–Diffusion Equation with Temporally Varying Coefficients

Author: Constance A. Ojwando, Mark Kimathi, John Awino

International Journal of Recent Research in Mathematics Computer Science and Information Technology

ISSN 2350-1022

Vol. 13, Issue 1, April 2026 - September 2026

Page No: 33-42

Paper Publications

Website: www.paperpublications.org

Published Date: 11-July-2026

Abstract: Road surface roughness is an important indicator for transportation safety, ride comfort, and pavement maintenance planning. Image-based three-dimensional reconstruction provides a low-cost and non-contact approach for generating dense road surface point clouds that can be analyzed geometrically. However, roughness values derived from point clouds are strongly affected by the neighborhood radius used during local surface analysis. This study investigates the influence of neighborhood radius on point-to-plane roughness estimation for a reconstructed asphalt road surface. This study focuses on the computational influence of neighborhood-scale selection in point-cloud geometric analysis. A road segment was reconstructed from smartphone imagery using a Structure-from-Motion and Multi-View Stereo workflow, and the resulting point cloud was processed in CloudCompare. After alignment, cropping, and surface normal estimation, roughness was computed at three neighborhood radii: 0.2, 0.4, and 0.6 model units. The results show that radius selection substantially changes both the spatial scalar-field representation and the mean roughness values. At the smallest radius, roughness computation is highly sensitive to fine-scale texture and local point-level variation. At larger radii, isolated high-frequency variation becomes less fragmented, while broader geometric undulations become more dominant. The mean roughness increased from 0.0225 at radius 0.2 to 0.0411 at radius 0.4 and 0.0602 at radius 0.6, indicating that larger neighborhoods captured broader surface deviation rather than only smoothing local texture. These findings confirm that point-cloud roughness is scale-dependent and should always be interpreted together with the selected neighborhood radius. The study provides practical guidance for CloudCompare-based roughness analysis in image-based road monitoring applications.

Keywords: road surface roughness; point cloud; CloudCompare; point-to-plane distance; neighborhood radius; multi-scale analysis; Structure-from-Motion.

Title: Scale-Dependent Point-Cloud Roughness Analysis for Image-Based 3D Road Surface Reconstruction

Author: Elmegdar Marouane

International Journal of Recent Research in Mathematics Computer Science and Information Technology

ISSN 2350-1022

Vol. 13, Issue 1, April 2026 - September 2026

Page No: 25-32

Paper Publications

Website: www.paperpublications.org

Published Date: 28-May-2026

Abstract: Deep reinforcement learning (DRL) has become a promising approach for wireless resource management because of its ability to adapt scheduling, power control, and allocation decisions under dynamic network conditions. However, many DRL-based wireless solutions optimize performance through reward shaping alone, which can make Quality-of-Service (QoS) constraints difficult to interpret, tune, or guarantee in practical deployments. This paper presents a review and design perspective on constraint-handling mechanisms for learning-based wireless resource management, with a particular focus on the comparison between built-in constrained reinforcement learning methods and external rule-based QoS governors. We discuss four major approaches: reward-penalty design, constrained Markov decision process formulations, safety-layer or shielding methods, and runtime QoS governor mechanisms. The analysis highlights that while constrained RL methods provide a principled mathematical framework, they may introduce additional training complexity and sensitivity to hyperparameter selection. In contrast, rule-based QoS governors offer a practical and interpretable way to monitor service degradation, enforce conservative recovery actions, and support deployment around legacy schedulers such as proportional fair scheduling. Based on this comparison, the paper argues that external QoS governors can serve as a useful middle layer between fully heuristic scheduling and fully autonomous learning-based control. Finally, we identify open challenges related to multi-cell coordination, real-time inference, traffic generalization, O-RAN integration, and standardized benchmarking for safe DRL-based wireless systems.

Keywords: Deep reinforcement learning, wireless resource management, QoS constraints, safe reinforcement learning, proportional fair scheduling, runtime governor, O-RAN.

Title: Rule-Based QoS Governors versus Built-in Constrained Reinforcement Learning for Wireless Resource Management: A Review and Design Perspective

Author: Aouari Abdelhamid, Yuting Li

International Journal of Recent Research in Mathematics Computer Science and Information Technology

ISSN 2350-1022

Vol. 13, Issue 1, April 2026 - September 2026

Page No: 18-24

Paper Publications

Website: www.paperpublications.org

Published Date: 04-May-2026

Abstract: The increasing complexity of modern projects has necessitated the development of advanced governance frameworks capable of supporting real-time monitoring, transparent decision-making, and efficient resource management. This study proposes a cloud-based project governance platform grounded in mathematical modeling and analytical techniques to enhance decision intelligence and monitoring of project deliverables. The framework models governance effectiveness as a dynamic system influenced by data integrity, monitoring efficiency, and risk exposure, while introducing a Governance Performance Function (GPF) for quantifying governance outcomes. In addition, a probabilistic Decision Reliability Model is developed to evaluate the accuracy and consistency of decisions under uncertainty. An optimization model is further incorporated to support efficient resource allocation within budgetary and operational constraints. Simulation results demonstrate that the proposed framework significantly improves governance performance, enhances transparency, and reduces risk compared to traditional systems. The integration of cloud infrastructure with mathematical and data-driven approaches ensures scalability, objectivity, and reproducibility in governance processes. The study concludes that the proposed model provides a robust foundation for advancing project governance toward a predictive, adaptive, and optimization-driven paradigm suitable for complex, data-intensive environments.

Keywords: Cloud-based governance; Decision reliability; Project monitoring; Optimization models; Data-driven decision making.

Title: Cloud-Based Project Governance Platforms for Data-Driven Decision Making and Transparent Monitoring of Project Deliverables: A Mathematical and Analytical Framework

Author: Nnenna Linda Akunna, Otugene Victor Bamigwojo

International Journal of Recent Research in Mathematics Computer Science and Information Technology

ISSN 2350-1022

Vol. 13, Issue 1, April 2026 - September 2026

Page No: 1-17

Paper Publications

Website: www.paperpublications.org

Published Date: 15-April-2026