Journal Description
Mathematical and Computational Applications
Mathematical and Computational Applications
is an international, peer-reviewed, open access journal on applications of mathematical and/or computational techniques, published bimonthly online by MDPI. The South African Association for Theoretical and Applied Mechanics (SAAM) is affiliated with the journal Mathematical and Computational Applications and its members receive discounts on the article processing charges.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, ESCI (Web of Science), Inspec, and other databases.
- Journal Rank: JCR - Q2 (Mathematics, Interdisciplinary Applications)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 25.3 days after submission; acceptance to publication is undertaken in 2.9 days (median values for papers published in this journal in the first half of 2025).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Testimonials: See what our editors and authors say about MCA.
Impact Factor:
2.1 (2024);
5-Year Impact Factor:
1.6 (2024)
Latest Articles
Last-Mile Decomposition Heuristics with Multi-Period Embedded Optimization Models
Math. Comput. Appl. 2025, 30(4), 90; https://doi.org/10.3390/mca30040090 (registering DOI) - 17 Aug 2025
Abstract
This paper investigates last-mile delivery and explores hybrid distributed computational models for routing and scheduling delivery services and assigning delivery-points to deliverymen over multiple time periods. The objective of these models is to minimize the number of deliverymen hired for providing delivery services
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This paper investigates last-mile delivery and explores hybrid distributed computational models for routing and scheduling delivery services and assigning delivery-points to deliverymen over multiple time periods. The objective of these models is to minimize the number of deliverymen hired for providing delivery services over multiple periods while satisfying predetermined time limits. This paper describes the development of multiple traveling deliverymen approaches, multi-period optimization models, and a multi-period distributed algorithm, to optimize routing and scheduling for last-mile deliveries. This paper utilizes a computer-aided modeling system to facilitate the proposed distributed approach, which offers an optimization model for large numbers of delivery-points and helps in performing limited computation as required to minimize the memory usage and provide efficiently solvable models within acceptable durations of execution. To illustrate the solvability of the proposed approach and scalability to large instances, 26 case problems are presented for last-mile delivery services. The key results include optimized routing and scheduling, a minimum number of deliverymen, and a significant reduction in computational effort and time.
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(This article belongs to the Section Engineering)
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Statistical Modeling of Reliable Intervals for Solutions to Linear Transfer Problems Under Boundary Experimental Data
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Olha Chernukha, Petro Pukach, Yurii Bilushchak, Halyna Bilushchak and Myroslava Vovk
Math. Comput. Appl. 2025, 30(4), 89; https://doi.org/10.3390/mca30040089 - 12 Aug 2025
Abstract
A methodology for the statistical modeling of boundary value problems of mathematical physics for parabolic equations used to describe transport processes in a layer with incomplete data at the boundary of a body has been developed and presented. The boundary value problem is
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A methodology for the statistical modeling of boundary value problems of mathematical physics for parabolic equations used to describe transport processes in a layer with incomplete data at the boundary of a body has been developed and presented. The boundary value problem is formulated for the case of a non-zero initial condition, the presence of a stable source at one boundary of the body (classical boundary condition), and a sample of experimental data for the desired function at the other boundary (statistical boundary condition). A linear regression model obtained from experimental data by the least squares method is used as a boundary condition. The article defines two-sided statistical estimates of the solution of the boundary value problem through linear regression coefficients, analyzes the mathematical model taking into account the influence of the sample size and covariance, determines the reliable intervals for linear regression and the desired function depending on the given level of reliability. The influence of the experimental data statistical characteristics on the desired function at the lower layer’s boundary for different types of samples in the case of large or small-time intervals is studied. The two-sided critical domain is obtained and analyzed on the basis of Fisher’s criterion. The influence of the reliability level on the reliable intervals, the solution to the parabolic boundary value problem, and the width of the bilateral critical domain constructed for the solution is analyzed.
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(This article belongs to the Special Issue Statistical Inference in Linear Models, 2nd Edition)
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Spherical Shape Functions for a Six-Node Tri-Rectangular Prism and an Eight-Node Quadrangular Right Prism
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Anna Maria Marotta, Riccardo Barzaghi and Roberto Sabadini
Math. Comput. Appl. 2025, 30(4), 88; https://doi.org/10.3390/mca30040088 - 10 Aug 2025
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In this work, we present the procedure to obtain exact spherical shape functions for finite element modeling applications, without resorting to any kind of approximation, for generic prismatic spherical elements and for the case of spherical six-node tri-rectangular and eight-node quadrangular spherical prisms.
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In this work, we present the procedure to obtain exact spherical shape functions for finite element modeling applications, without resorting to any kind of approximation, for generic prismatic spherical elements and for the case of spherical six-node tri-rectangular and eight-node quadrangular spherical prisms. The proposed spherical shape functions, given in explicit analytical form, are expressed in geographic coordinates, namely colatitude, longitude and distance from the center of the sphere. We demonstrate that our analytical shape functions satisfy all the properties required by this class of functions, deriving at the same time the analytical expression of the Jacobian, which allows us changes in coordinate systems. Within the perspective of volume integration on Earth, entering a variety of geophysical and geodetic problems, as for mass change contribution to gravity, we consider our analytical expression of the shape functions and Jacobian for the six-node tri-rectangular and eight-node quadrangular right spherical prisms as reference volumes to evaluate the volume of generic spherical triangular and quadrangular prisms over the sphere; volume integration is carried out via Gauss–Legendre quadrature points. We show that for spherical quadrangular prisms, the percentage volume difference between the exact and the numerically evaluated volumes is independent from both the geographical position and the depth and ranges from 10−3 to lower than 10−4 for angular dimensions ranging from 1° × 1° to 0.25° × 0.25°. A satisfactory accuracy is attained for eight Gauss–Legendre quadrature points. We also solve the Poisson equation and compare the numerical solution with the analytical solution, obtained in the case of steady-state heat conduction with internal heat production. We show that, even with a relatively coarse grid, our elements are capable of providing a satisfactory fit between numerical and analytical solutions, with a maximum difference in the order of 0.2% of the exact value.
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Modified Engel Algorithm and Applications in Absorbing/Non-Absorbing Markov Chains and Monopoly Game
by
Chunhe Liu and Jeff Chak Fu Wong
Math. Comput. Appl. 2025, 30(4), 87; https://doi.org/10.3390/mca30040087 - 8 Aug 2025
Abstract
The Engel algorithm was created to solve chip-firing games and can be used to find the stationary distribution for absorbing Markov chains. Kaushal et al. developed a matlab-based version of the generalized Engel algorithm based on Engel’s probabilistic abacus theory. This paper
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The Engel algorithm was created to solve chip-firing games and can be used to find the stationary distribution for absorbing Markov chains. Kaushal et al. developed a matlab-based version of the generalized Engel algorithm based on Engel’s probabilistic abacus theory. This paper introduces a modified version of the generalized Engel algorithm, which we call the modified Engel algorithm, or the mEngel algorithm for short. This modified version is designed to address issues related to non-absorbing Markov chains. It achieves this by breaking down the transition matrix into two distinct matrices, where each entry in the transition matrix is calculated from the ratio of the numerator and denominator matrices. In a nested iteration setting, these matrices play a crucial role in converting non-absorbing Markov chains into absorbing ones and then back again, thereby providing an approximation of the solutions of non-absorbing Markov chains until the distribution of a Markov chain converges to a stationary distribution. Our results show that the numerical outcomes of the mEngel algorithm align with those obtained from the power method and the canonical decomposition of absorbing Markov chains. We provide an example, Torrence’s problem, to illustrate the application of absorbing probabilities. Furthermore, our proposed algorithm analyzes the Monopoly transition matrix as a form of non-absorbing probabilities based on the rules of the Monopoly game, a complete information dynamic game, particularly the probability of landing on the Jail square, which is determined by the order of the product of the movement, Jail, Chance, and Community Chest matrices. The Long Jail strategy, the Short Jail strategy, and the strategy for getting out of Jail by rolling consecutive doubles three times have been formulated and tested. In addition, choosing which color group to buy is also an important strategy. By comparing the probability distribution of each strategy and the profit return for each property and color group of properties, and the color group property, we find which one should be used when playing Monopoly. In conclusion, the mEngel algorithm, implemented using R codes, offers an alternative approach to solving the Monopoly game and demonstrates practical value.
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(This article belongs to the Section Engineering)
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Computing Two Heuristic Shrinkage Penalized Deep Neural Network Approach
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Mostafa Behzadi, Saharuddin Bin Mohamad, Mahdi Roozbeh, Rossita Mohamad Yunus and Nor Aishah Hamzah
Math. Comput. Appl. 2025, 30(4), 86; https://doi.org/10.3390/mca30040086 - 7 Aug 2025
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Linear models are not always able to sufficiently capture the structure of a dataset. Sometimes, combining predictors in a non-parametric method, such as deep neural networks (DNNs), would yield a more flexible modeling of the response variables in the predictions. Furthermore, the standard
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Linear models are not always able to sufficiently capture the structure of a dataset. Sometimes, combining predictors in a non-parametric method, such as deep neural networks (DNNs), would yield a more flexible modeling of the response variables in the predictions. Furthermore, the standard statistical classification or regression approaches are inefficient when dealing with more complexity, such as a high-dimensional problem, which usually suffers from multicollinearity. For confronting these cases, penalized non-parametric methods are very useful. This paper proposes two heuristic approaches and implements new shrinkage penalized cost functions in the DNN, based on the elastic-net penalty function concept. In other words, some new methods via the development of shirnkaged penalized DNN, such as and , are established, which are strong rivals for and . If there is any dataset grouping information in each layer of the DNN, it may be transferred using the derived penalized function of elastic-net; other penalized DNNs cannot provide this functionality. Regarding the outcomes in the tables, in the developed DNN, not only are there slight increases in the classification results, but there are also nullifying processes of some nodes in addition to a shrinkage property simultaneously in the structure of each layer. A simulated dataset was generated with the binary response variables, and the classic and heuristic shrinkage penalized DNN models were generated and tested. For comparison purposes, the DNN models were also compared to the classification tree using GUIDE and applied to a real microbiome dataset.
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Mathematical Modelling of Upper Room UVGI in UFAD Systems for Enhanced Energy Efficiency and Airborne Disease Control: Applications for COVID-19 and Tuberculosis
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Mohamad Kanaan, Eddie Gazo-Hanna and Semaan Amine
Math. Comput. Appl. 2025, 30(4), 85; https://doi.org/10.3390/mca30040085 - 5 Aug 2025
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This study is the first to investigate the performance of ultraviolet germicidal irradiation (UVGI) in underfloor air distribution (UFAD) systems. A simplified mathematical model is developed to predict airborne pathogen transport and inactivation by upper room UVGI in UFAD spaces. The proposed model
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This study is the first to investigate the performance of ultraviolet germicidal irradiation (UVGI) in underfloor air distribution (UFAD) systems. A simplified mathematical model is developed to predict airborne pathogen transport and inactivation by upper room UVGI in UFAD spaces. The proposed model is substantiated for the SARS-CoV-2 virus as a simulated pathogen through a comprehensive computational fluid dynamics methodology validated against published experimental data of upper room UVGI and UFAD flows. Simulations show an 11% decrease in viral concentration within the upper irradiated zone when a 15 W louvered germicidal lamp is utilized. Finally, a case study on Mycobacterium tuberculosis (M. tuberculosis) bacteria is carried out using the validated simplified model to optimize the use of return air and UVGI implementation, ensuring acceptable indoor air quality and enhanced energy efficiency. Results reveal that the UFAD-UVGI system may consume up to 13.6% less energy while keeping the occupants at acceptable levels of M. tuberculosis concentration and UV irradiance when operated with 26% return air and a UVGI output of 72 W.
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Adaptive Filtered-x Least Mean Square Algorithm to Improve the Performance of Multi-Channel Noise Control Systems
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Maha Yousif Hasan, Ahmed Sabah Alaraji, Amjad J. Humaidi and Huthaifa Al-Khazraji
Math. Comput. Appl. 2025, 30(4), 84; https://doi.org/10.3390/mca30040084 - 5 Aug 2025
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This paper proposes an optimized control filter (OCF) based on the Filtered-x Least Mean Square (FxLMS) algorithm for multi-channel active noise control (ANC) systems. The proposed OCF-McFxLMS algorithm delivers three key contributions. Firstly, even in difficult noise situations such as White Gaussian, Brownian,
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This paper proposes an optimized control filter (OCF) based on the Filtered-x Least Mean Square (FxLMS) algorithm for multi-channel active noise control (ANC) systems. The proposed OCF-McFxLMS algorithm delivers three key contributions. Firstly, even in difficult noise situations such as White Gaussian, Brownian, and pink noise, it greatly reduces error, reaching nearly zero mean squared error (MSE) values across all Microphone (Mic) channels. Secondly, it improves computational efficiency by drastically reducing execution time from 58.17 s in the standard McFxLMS algorithm to just 0.0436 s under White Gaussian noise, enabling real-time noise control without compromising accuracy. Finally, the OCF-McFxLMS demonstrates robust noise attenuation, achieving signal-to-noise ratio (SNR) values of 137.41 dB under White Gaussian noise and over 100 dB for Brownian and pink noise, consistently outperforming traditional approaches. These contributions collectively establish the OCF-McFxLMS algorithm as an efficient and effective solution for real-time ANC systems, delivering superior noise reduction and computational speed performance across diverse noise environments.
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A Hybrid Deep Reinforcement Learning Architecture for Optimizing Concrete Mix Design Through Precision Strength Prediction
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Ali Mirzaei and Amir Aghsami
Math. Comput. Appl. 2025, 30(4), 83; https://doi.org/10.3390/mca30040083 - 3 Aug 2025
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Concrete mix design plays a pivotal role in ensuring the mechanical performance, durability, and sustainability of construction projects. However, the nonlinear interactions among the mix components challenge traditional approaches in predicting compressive strength and optimizing proportions. This study presents a two-stage hybrid framework
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Concrete mix design plays a pivotal role in ensuring the mechanical performance, durability, and sustainability of construction projects. However, the nonlinear interactions among the mix components challenge traditional approaches in predicting compressive strength and optimizing proportions. This study presents a two-stage hybrid framework that integrates deep learning with reinforcement learning to overcome these limitations. First, a Convolutional Neural Network–Long Short-Term Memory (CNN–LSTM) model was developed to capture spatial–temporal patterns from a dataset of 1030 historical concrete samples. The extracted features were enhanced using an eXtreme Gradient Boosting (XGBoost) meta-model to improve generalizability and noise resistance. Then, a Dueling Double Deep Q-Network (Dueling DDQN) agent was used to iteratively identify optimal mix ratios that maximize the predicted compressive strength. The proposed framework outperformed ten benchmark models, achieving an MAE of 2.97, RMSE of 4.08, and R2 of 0.94. Feature attribution methods—including SHapley Additive exPlanations (SHAP), Elasticity-Based Feature Importance (EFI), and Permutation Feature Importance (PFI)—highlighted the dominant influence of cement content and curing age, as well as revealing non-intuitive effects such as the compensatory role of superplasticizers in low-water mixtures. These findings demonstrate the potential of the proposed approach to support intelligent concrete mix design and real-time optimization in smart construction environments.
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(This article belongs to the Section Engineering)
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Energy Management and Power Distribution for Battery/Ultracapacitor Hybrid Energy Storage System in Electric Vehicles with Regenerative Braking Control
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Abdelsalam A. Ahmed, Young Il Lee, Saleh Al Dawsari, Ahmed A. Zaki Diab and Abdelsalam A. Ezzat
Math. Comput. Appl. 2025, 30(4), 82; https://doi.org/10.3390/mca30040082 - 3 Aug 2025
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This paper presents an advanced energy management system (EMS) for optimizing power distribution in a battery/ultracapacitor (UC) hybrid energy storage system (HESS) for electric vehicles (EVs). The proposed EMS accounts for all energy flow scenarios within a practical driving cycle. A regenerative braking
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This paper presents an advanced energy management system (EMS) for optimizing power distribution in a battery/ultracapacitor (UC) hybrid energy storage system (HESS) for electric vehicles (EVs). The proposed EMS accounts for all energy flow scenarios within a practical driving cycle. A regenerative braking control strategy is developed to maximize kinetic energy recovery using an induction motor, efficiently distributing the recovered energy between the UC and battery. Additionally, a power flow management approach is introduced for both motoring (discharge) and braking (charge) operations via bidirectional buck–boost DC-DC converters. In discharge mode, an optimal distribution factor is dynamically adjusted to balance power delivery between the battery and UC, maximizing efficiency. During charging, a DC link voltage control mechanism prioritizes UC charging over the battery, reducing stress and enhancing energy recovery efficiency. The proposed EMS is validated through simulations and experiments, demonstrating significant improvements in vehicle acceleration, energy efficiency, and battery lifespan.
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(This article belongs to the Special Issue Applied Optimization in Automatic Control and Systems Engineering)
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Intermittent and Adaptive Control Strategies for Chaos Suppression in a Cancer Model
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Rugilė Jonuškaitė and Inga Telksnienė
Math. Comput. Appl. 2025, 30(4), 81; https://doi.org/10.3390/mca30040081 - 3 Aug 2025
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The chaotic dynamics observed in mathematical models of cancer can correspond to the unpredictable tumor growth and treatment responses seen in clinical settings. Suppressing this chaos is a significant challenge in theoretical oncology. This paper investigates and compares four distinct control strategies designed
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The chaotic dynamics observed in mathematical models of cancer can correspond to the unpredictable tumor growth and treatment responses seen in clinical settings. Suppressing this chaos is a significant challenge in theoretical oncology. This paper investigates and compares four distinct control strategies designed to stabilize a chaotic three-dimensional tumor-immune interaction model. The objective is to steer the system from its chaotic attractor to a target unstable periodic orbit, representing a transition to a more regular and predictable dynamic. The strategies, all based on the external force control paradigm, include continuous control, a simple state-dependent intermittent control, an improved intermittent control with a minimum activation duration to suppress chattering, and an adaptive intermittent control with a time-varying feedback gain. The performance of each strategy is quantitatively evaluated based on tracking accuracy and the required control effort.
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Dynamics of a Fractional-Order Within-Host Virus Model with Adaptive Immune Responses and Two Routes of Infection
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Taofeek O. Alade, Furaha M. Chuma, Muhammad Javed, Samson Olaniyi, Adekunle O. Sangotola and Gideon K. Gogovi
Math. Comput. Appl. 2025, 30(4), 80; https://doi.org/10.3390/mca30040080 - 2 Aug 2025
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This paper introduces a novel fractional-order model using the Caputo derivative operator to investigate the virus dynamics of adaptive immune responses. Two infection routes, namely cell-to-cell and virus-to-cell transmissions, are incorporated into the dynamics. Our research establishes the existence and uniqueness of positive
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This paper introduces a novel fractional-order model using the Caputo derivative operator to investigate the virus dynamics of adaptive immune responses. Two infection routes, namely cell-to-cell and virus-to-cell transmissions, are incorporated into the dynamics. Our research establishes the existence and uniqueness of positive and bounded solutions through the application of the generalized mean-value theorem and Banach fixed-point theory methods. The fractional-order model is shown to be Ulam–Hyers stable, ensuring the model’s resilience to small errors. By employing the normalized forward sensitivity method, we identify critical parameters that profoundly influence the transmission dynamics of the fractional-order virus model. Additionally, the framework of optimal control theory is used to explore the characterization of optimal adaptive immune responses, encompassing antibodies and cytotoxic T lymphocytes (CTL). To assess the influence of memory effects, we utilize the generalized forward–backward sweep technique to simulate the fractional-order virus dynamics. This study contributes to the existing body of knowledge by providing insights into how the interaction between virus-to-cell and cell-to-cell dynamics within the host is affected by memory effects in the presence of optimal control, reinforcing the invaluable synergy between fractional calculus and optimal control theory in modeling within-host virus dynamics, and paving the way for potential control strategies rooted in adaptive immunity and fractional-order modeling.
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Enhanced Exact Methods for Optimizing Energy Delivery in Preemptive Electric Vehicle Charging Scheduling Problems
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Abdennour Azerine, Mahmoud Golabi, Ammar Oulamara and Lhassane Idoumghar
Math. Comput. Appl. 2025, 30(4), 79; https://doi.org/10.3390/mca30040079 - 24 Jul 2025
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The increasing adoption of electric vehicles (EVs) requires efficient management of charging infrastructure, particularly in optimizing the allocation of limited charging resources. This paper addresses the preemptive electric vehicle charging scheduling problem (EVCSP), where charging sessions can be interrupted to maximize the number
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The increasing adoption of electric vehicles (EVs) requires efficient management of charging infrastructure, particularly in optimizing the allocation of limited charging resources. This paper addresses the preemptive electric vehicle charging scheduling problem (EVCSP), where charging sessions can be interrupted to maximize the number of satisfied demands. The existing mathematical formulations often struggle with scalability and computational efficiency for even small problem instances. As a result, we propose an enhanced mathematical programming model, which is further refined to reduce decision variable complexity and improve computational performance. In addition, a constraint programming (CP) approach is explored as an alternative method for solving the EVCSP due to its strength in handling complex scheduling constraints. The experimental results demonstrate that the developed methods significantly outperform the existing models in the literature, providing scalable and efficient solutions for optimizing EV charging infrastructure.
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Unmanned Aerial Vehicle Position Tracking Using Nonlinear Autoregressive Exogenous Networks Learned from Proportional-Derivative Model-Based Guidance
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Wilson Pavon, Jorge Chavez, Diego Guffanti and Ama Baduba Asiedu-Asante
Math. Comput. Appl. 2025, 30(4), 78; https://doi.org/10.3390/mca30040078 - 24 Jul 2025
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The growing demand for agile and reliable Unmanned Aerial Vehicles (UAVs) has spurred the advancement of advanced control strategies capable of ensuring stability and precision under nonlinear and uncertain flight conditions. This work addresses the challenge of accurately tracking UAV position by proposing
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The growing demand for agile and reliable Unmanned Aerial Vehicles (UAVs) has spurred the advancement of advanced control strategies capable of ensuring stability and precision under nonlinear and uncertain flight conditions. This work addresses the challenge of accurately tracking UAV position by proposing a neural-network-based approach designed to replicate the behavior of classical control systems. A complete nonlinear model of the quadcopter was derived and linearized around a hovering point to design a traditional proportional derivative (PD) controller, which served as a baseline for training a nonlinear autoregressive exogenous (NARX) artificial neural network. The NARX model, selected for its feedback structure and ability to capture temporal dynamics, was trained to emulate the control signals of the PD controller under varied reference trajectories, including step, sinusoidal, and triangular inputs. The trained networks demonstrated performance comparable to the PD controller, particularly in the vertical axis, where the NARX model achieved a minimal Mean Squared Error (MSE) of and an value of 0.9852. These results confirm that the NARX neural network, trained via supervised learning to emulate a PD controller, can replicate and even improve classical control strategies in nonlinear scenarios, thereby enhancing robustness against dynamic changes and modeling uncertainties. This research contributes a scalable approach for integrating neural models into UAV control systems, offering a promising path toward adaptive and autonomous flight control architectures that maintain stability and accuracy in complex environments.
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(This article belongs to the Section Engineering)
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A High-Order Proper Orthogonal Decomposition Dimensionality Reduction Compact Finite-Difference Method for Diffusion Problems
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Wenqian Zhang and Hong Li
Math. Comput. Appl. 2025, 30(4), 77; https://doi.org/10.3390/mca30040077 - 23 Jul 2025
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An innovative high-order dimensionality reduction approach, which integrates a condensed finite-difference scheme with proper orthogonal decomposition techniques, has been explored for solving diffusion equations. The difference scheme with forth order accurate in both space and time is introduced through the idea of interpolation
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An innovative high-order dimensionality reduction approach, which integrates a condensed finite-difference scheme with proper orthogonal decomposition techniques, has been explored for solving diffusion equations. The difference scheme with forth order accurate in both space and time is introduced through the idea of interpolation approximation. The quartic spline function and Padé approximation were utilized in space and time discretization, respectively. The stability and convergence were proven. Moreover, the dimensionality reduction formulas were derived using the proper orthogonal decomposition (POD) method, which is based on the matrix representation of the compact finite-difference scheme. The bases of the POD method were established by cumulative contribution rate of the eigenvalues of snapshot matrix that is different from the traditional ways in which the bases were established by the first eigenvalues. The method of cumulative contribution rate can optimize the degree of freedom. The error analysis of the reduced bases high-order POD finite-difference scheme was provided. Numerical experiments are conducted to validate the soundness and dependability of the reduced-order algorithm. The comparisons between the finite-difference method, the traditional POD method, and reduced dimensional method with cumulative contribution rate were discussed.
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Enhanced BiCGSTAB with Restrictive Preconditioning for Nonlinear Systems: A Mean Curvature Image Deblurring Approach
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Rizwan Khalid, Shahbaz Ahmad, Iftikhar Ali and Manuel De la Sen
Math. Comput. Appl. 2025, 30(4), 76; https://doi.org/10.3390/mca30040076 - 17 Jul 2025
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We present an advanced restrictively preconditioned biconjugate gradient-stabilized (RPBiCGSTAB) algorithm specifically designed to improve the convergence speed of Krylov subspace methods for nonlinear systems characterized by a structured 5-by-5 block configuration. This configuration frequently arises from cell-centered finite difference discretizations employed in solving
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We present an advanced restrictively preconditioned biconjugate gradient-stabilized (RPBiCGSTAB) algorithm specifically designed to improve the convergence speed of Krylov subspace methods for nonlinear systems characterized by a structured 5-by-5 block configuration. This configuration frequently arises from cell-centered finite difference discretizations employed in solving image deblurring problems governed by mean curvature dynamics. The RPBiCGSTAB method is crafted to exploit this block structure, thereby optimizing both computational efficiency and convergence behavior in complex image processing tasks. Analyzing the spectral characteristics of preconditioned matrices often reveals a beneficial distribution of eigenvalues, which plays a critical role in accelerating the convergence of the RPBiCGSTAB algorithm. Furthermore, our numerical experiments validate the computational efficiency and practical applicability of the method in addressing nonlinear systems commonly encountered in image deblurring. Our analysis also extends to the spectral properties of the preconditioned matrices, noting a pronounced clustering of eigenvalues around 1, which contributes to enhanced stability and convergence performance.Through numerical simulations that focus on mean curvature-driven image deblurring, we highlight the superior performance of the RPBiCGSTAB method in comparison to other techniques in this specialized field.
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Decoding Retail Commerce Patterns with Multisource Urban Knowledge
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Tianchu Xia, Yixue Chen, Fanru Gao, Yuk Ting Hester Chow, Jianjing Zhang and K. L. Keung
Math. Comput. Appl. 2025, 30(4), 75; https://doi.org/10.3390/mca30040075 - 17 Jul 2025
Abstract
Urban commercial districts, with their unique characteristics, serve as a reflection of broader urban development patterns. However, only a handful of studies have harnessed point-of-interest (POI) data to model the intricate relationship between retail commercial space types and other factors. This paper endeavors
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Urban commercial districts, with their unique characteristics, serve as a reflection of broader urban development patterns. However, only a handful of studies have harnessed point-of-interest (POI) data to model the intricate relationship between retail commercial space types and other factors. This paper endeavors to bridge this gap, focusing on the influence of urban development factors on retail commerce districts through the lens of POI data. Our exploration underscores how commercial zones impact the density of residential neighborhoods and the coherence of pedestrian pathways. To facilitate our investigation, we propose an ensemble clustering technique for identifying and outlining urban commercial areas, including Kernel Density Analysis (KDE), Density-based Spatial Clustering of Applications with Noise (DBSCAN), Geographically Weighted Regression (GWR). Our research uses the city of Manchester as a case study, unearthing the relationship between commercial retail catchment areas and a range of factors (retail commercial space types, land use function, walking coverage). These include land use function, walking coverage, and green park within the specified areas. As we explore the multiple impacts of different urban development factors on retail commerce models, we hope this study acts as a springboard for further exploration of the untapped potential of POI data in urban business development and planning.
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(This article belongs to the Section Engineering)
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Testing Neural Architecture Search Efficient Evaluation Methods in DeepGA
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Jesús-Arnulfo Barradas-Palmeros, Carlos-Alberto López-Herrera, Efrén Mezura-Montes, Héctor-Gabriel Acosta-Mesa and Adriana-Laura López-Lobato
Math. Comput. Appl. 2025, 30(4), 74; https://doi.org/10.3390/mca30040074 - 17 Jul 2025
Abstract
Neural Architecture search (NAS) aims to automate the design process of Deep Neural Networks, reducing the Deep Learning (DL) expertise required and avoiding a trial-and-error process. Nonetheless, one of the main drawbacks of NAS is the high consumption of computational resources. Consequently, efficient
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Neural Architecture search (NAS) aims to automate the design process of Deep Neural Networks, reducing the Deep Learning (DL) expertise required and avoiding a trial-and-error process. Nonetheless, one of the main drawbacks of NAS is the high consumption of computational resources. Consequently, efficient evaluation methods (EEMs) to assess the quality of candidate architectures are an open research problem. This work tests various EEMs in the Deep Genetic Algorithm (DeepGA), including early stopping, population memory, and training-free proxies. The Fashion MNIST, CIFAR-10, and CIFAR-100 datasets were used for experimentation. The results show that population memory has a valuable impact on avoiding repeated evaluations. Additionally, early stopping achieved competitive performance while significantly reducing the computational cost of the search process. The training-free configurations using the Logsynflow and Linear Regions proxies, as well as a combination of both, were only partially competitive but dramatically reduced the search time. Finally, a comparison of the architectures and hyperparameters obtained with the different algorithm configurations is presented. The training-free search processes resulted in deeper architectures with more fully connected layers and skip connections than the ones obtained with accuracy-guided search configurations.
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(This article belongs to the Special Issue Feature Papers in Mathematical and Computational Applications 2025)
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Secure Communication of Electric Drive System Using Chaotic Systems Base on Disturbance Observer and Fuzzy Brain Emotional Learning Neural Network
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Huyen Chau Phan Thi, Nhat Quang Dang and Van Nam Giap
Math. Comput. Appl. 2025, 30(4), 73; https://doi.org/10.3390/mca30040073 - 14 Jul 2025
Abstract
This paper presents a novel wireless control framework for electric drive systems by employing a fuzzy brain emotional learning neural network (FBELNN) controller in conjunction with a Disturbance Observer (DO). The communication scheme uses chaotic system dynamics to ensure data confidentiality and robustness
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This paper presents a novel wireless control framework for electric drive systems by employing a fuzzy brain emotional learning neural network (FBELNN) controller in conjunction with a Disturbance Observer (DO). The communication scheme uses chaotic system dynamics to ensure data confidentiality and robustness against disturbance in wireless environments. To be applied to embedded microprocessors, the continuous-time chaotic system is discretized using the Grunwald–Letnikov approximation. To avoid the loss of generality of chaotic behavior, Lyapunov exponents are computed to validate the preservation of chaos in the discrete-time domain. The FBELNN controller is then developed to synchronize two non-identical chaotic systems under different initial conditions, enabling secure data encryption and decryption. Additionally, the DOB is introduced to estimate and mitigate the effects of bounded uncertainties and external disturbances, enhancing the system’s resilience to stealthy attacks. The proposed control structure is experimentally implemented on a wireless communication system utilizing ESP32 microcontrollers (Espressif Systems, Shanghai, China) based on the ESP-NOW protocol. Both control and feedback signals of the electric drive system are encrypted using chaotic states, and real-time decryption at the receiver confirms system integrity. Experimental results verify the effectiveness of the proposed method in achieving robust synchronization, accurate signal recovery, and a reliable wireless control system. The combination of FBELNN and DOB demonstrates significant potential for real-time, low-cost, and secure applications in smart electric drive systems and industrial automation.
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(This article belongs to the Special Issue Applied Optimization in Automatic Control and Systems Engineering)
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Physics-Informed Neural Network for Nonlinear Bending Analysis of Nano-Beams: A Systematic Hyperparameter Optimization
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Saba Sadat Mirsadeghi Esfahani, Ali Fallah and Mohammad Mohammadi Aghdam
Math. Comput. Appl. 2025, 30(4), 72; https://doi.org/10.3390/mca30040072 - 14 Jul 2025
Abstract
This paper investigates the nonlinear bending analysis of nano-beams using the physics-informed neural network (PINN) method. The nonlinear governing equations for the bending of size-dependent nano-beams are derived from Hamilton’s principle, incorporating nonlocal strain gradient theory, and based on Euler–Bernoulli beam theory. In
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This paper investigates the nonlinear bending analysis of nano-beams using the physics-informed neural network (PINN) method. The nonlinear governing equations for the bending of size-dependent nano-beams are derived from Hamilton’s principle, incorporating nonlocal strain gradient theory, and based on Euler–Bernoulli beam theory. In the PINN method, the solution is approximated by a deep neural network, with network parameters determined by minimizing a loss function that consists of the governing equation and boundary conditions. Despite numerous reports demonstrating the applicability of the PINN method for solving various engineering problems, tuning the network hyperparameters remains challenging. In this study, a systematic approach is employed to fine-tune the hyperparameters using hyperparameter optimization (HPO) via Gaussian process-based Bayesian optimization. Comparison of the PINN results with available reference solutions shows that the PINN, with the optimized parameters, produces results with high accuracy. Finally, the impacts of boundary conditions, different loads, and the influence of nonlocal strain gradient parameters on the bending behavior of nano-beams are investigated.
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(This article belongs to the Special Issue Advances in Computational and Applied Mechanics (SACAM))
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Permeability Prediction Using Vision Transformers
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Cenk Temizel, Uchenna Odi, Kehao Li, Lei Liu, Salih Tutun and Javier Santos
Math. Comput. Appl. 2025, 30(4), 71; https://doi.org/10.3390/mca30040071 - 8 Jul 2025
Abstract
Accurate permeability predictions remain pivotal for understanding fluid flow in porous media, influencing crucial operations across petroleum engineering, hydrogeology, and related fields. Traditional approaches, while robust, often grapple with the inherent heterogeneity of reservoir rocks. With the advent of deep learning, convolutional neural
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Accurate permeability predictions remain pivotal for understanding fluid flow in porous media, influencing crucial operations across petroleum engineering, hydrogeology, and related fields. Traditional approaches, while robust, often grapple with the inherent heterogeneity of reservoir rocks. With the advent of deep learning, convolutional neural networks (CNNs) have emerged as potent tools in image-based permeability estimation, capitalizing on micro-CT scans and digital rock imagery. This paper introduces a novel paradigm, employing vision transformers (ViTs)—a recent advancement in computer vision—for this crucial task. ViTs, which segment images into fixed-sized patches and process them through transformer architectures, present a promising alternative to CNNs. We present a methodology for implementing ViTs for permeability prediction, its results on diverse rock samples, and a comparison against conventional CNNs. The prediction results suggest that, with adequate training data, ViTs can match or surpass the predictive accuracy of CNNs, especially in rocks exhibiting significant heterogeneity. This study underscores the potential of ViTs as an innovative tool in permeability prediction, paving the way for further research and integration into mainstream reservoir characterization workflows.
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(This article belongs to the Special Issue Feature Papers in Mathematical and Computational Applications 2025)
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