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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 25.4 days after submission; acceptance to publication is undertaken in 2.6 days (median values for papers published in this journal in the second half of 2024).
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: 1.9 (2023); 5-Year Impact Factor: 1.6 (2023)

Imprint Information Journal Flyer Open Access ISSN: 2297-8747

Latest Articles

19 pages, 2800 KiB

Open AccessArticle

Impact Loading on a Patient-Specific Head Model: The Significance of Brain Constitutive Models and Loading Location

by Amirhossein Gandomirouzbahani, Hadi Taghizadeh, Iman Z. Oskui and Fábio A.O. Fernandes

Math. Comput. Appl. 2025, 30(2), 21; https://doi.org/10.3390/mca30020021 - 21 Feb 2025

Head impacts are common incidents that may cause traumatic brain injury (TBI), which imposes significant economic and social burdens. This study developed a patient-specific head model to address the significance of the brain’s constitutive model and loading location on head impact. Two hyperelastic [...] Read more.

Head impacts are common incidents that may cause traumatic brain injury (TBI), which imposes significant economic and social burdens. This study developed a patient-specific head model to address the significance of the brain’s constitutive model and loading location on head impact. Two hyperelastic (Model I and Model II) constitutive models and one hyper-viscoelastic (Model III) constitutive model for the brain tissue were developed. In Models II and III, white and gray matter heterogeneities were included. Respective volumetric and deviatoric responses were compared for a frontal head impact. Then, the load was applied to the head’s frontal, lateral, and posterior regions to report location-wise outcomes. The findings indicated that Model I, which was based on almost quasi-static experiments, underestimated the deviatoric responses. Although the pressure contours were similar for Models II and III, the latter included viscous effects and provided more accurate deviatoric responses. Lateral loading indicated a significantly higher risk of TBI. Interestingly, the deviatoric responses and strain energy density of the brain did not decay with relaxation of the impact load. Hence, the incidence of TBI should be explored after load relaxation. Full article

(This article belongs to the Special Issue Feature Papers in Mathematical and Computational Applications 2025)

15 pages, 3748 KiB

Open AccessArticle

Control Strategy of a Rotating Power Flow Controller Based on an Improved Hybrid Particle Swarm Optimization Algorithm

by Ziyang Zhang, Jiaoxin Jia, Waseem Aslam, Abubakar Siddique and Fahad R. Albogamy

Math. Comput. Appl. 2025, 30(1), 20; https://doi.org/10.3390/mca30010020 - 19 Feb 2025

As the proportion of renewable energy sources integrated into the power grid increases, it imposes significant volatility on the grid, leading to uneven load distribution across certain transmission lines. Rotating Power Flow Controllers (RPFCs) based on Rotating Phase-Shifting Transformers (RPSTs) offer a viable [...] Read more.

As the proportion of renewable energy sources integrated into the power grid increases, it imposes significant volatility on the grid, leading to uneven load distribution across certain transmission lines. Rotating Power Flow Controllers (RPFCs) based on Rotating Phase-Shifting Transformers (RPSTs) offer a viable solution to such issues in lines rated at 10 kV and below. This paper begins with a brief introduction to RPFCs, followed by the modeling of their topology for a single-circuit line and the derivation of active and reactive power flow formulas. Notably, this paper introduces intelligent optimization algorithms to this field for the first time, employing an improved hybrid particle swarm optimization (HPSO) algorithm to control the active power while keeping the reactive power constant and subsequently adjusting the reactive power while maintaining the active power steady, thereby achieving power regulation. Using Matlab/Simulink simulations, this strategy was compared with adaptive adjustment strategies, verifying that it exhibits reduced power fluctuations and overshoots during the adjustment process, thus confirming the effectiveness of the adjustment scheme. By leveraging this algorithm in conjunction with simulations, a Q-P operating range diagram for transmission lines was plotted, determining the adjustable range of actual power. Full article

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22 pages, 3960 KiB

Open AccessArticle

Vibration Control of Light Bridges Under Moving Loads Using Nonlinear Semi-Active Absorbers

by Hamed Saber, Farhad S. Samani, Francesco Pellicano, Moslem Molaie and Antonio Zippo

Math. Comput. Appl. 2025, 30(1), 19; https://doi.org/10.3390/mca30010019 - 14 Feb 2025

The dynamic response of light bridges to moving loads presents significant challenges in controlling vibrations that can impact on the structural integrity and the user comfort. This study investigates the effectiveness of nonlinear semi-active absorbers in mitigating these vibrations on light bridges that [...] Read more.

The dynamic response of light bridges to moving loads presents significant challenges in controlling vibrations that can impact on the structural integrity and the user comfort. This study investigates the effectiveness of nonlinear semi-active absorbers in mitigating these vibrations on light bridges that are particularly susceptible to human-induced vibrations, due to their inherent low damping and flexibility, especially under near-resonance conditions. Traditional passive vibration control methods, such as dynamic vibration absorbers (DVAs), may not be entirely adequate for mitigating vibrations, as they require adjustments in damping and stiffness when operating conditions change over time. Therefore, suitable strategies are needed to dynamically adapt DVA parameters and ensure optimal performance. This paper explores the effectiveness of linear and nonlinear DVAs in reducing vertical vibrations of lightweight beams subjected to moving loads. Using the Bubnov-Galerkin method, the governing partial differential equations are reduced to a set of ordinary differential equations and a novel nonlinear DVA with a variable damping dashpot is investigated, showing better performances compared to traditional constant-parameter DVAs. The nonlinear viscous damping device enables real-time adjustments, making the DVA semi-active and more effective. A footbridge case study demonstrates significant vibration reductions using optimized nonlinear DVAs for lightweight bridges, showing broader frequency effectiveness than linear ones. The quadratic nonlinear DVA is the most efficient, achieving a 92% deflection reduction in the 1.5–2.5 Hz range, and under running and jumping reduces deflection by 42%. Full article

(This article belongs to the Special Issue Mathematical and Computational Approaches in Applied Mechanics: A Themed Issue Dedicated to Professor J.N. Reddy)

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21 pages, 5113 KiB

Open AccessArticle

Mode Shape Projection for Damage Detection of Laminated Composite Plates

by Morteza Saadatmorad, Mohammad-Hadi Pashaei, Ramazan-Ali Jafari-Talookolaei and Samir Khatir

Math. Comput. Appl. 2025, 30(1), 18; https://doi.org/10.3390/mca30010018 - 11 Feb 2025

The wavelet technique has limitations in detecting damage at the edges of two-dimensional signals. This weakness arises from the nature of the wavelet transform procedure, which shifts the signal by differencing the signal’s pair arrays in the neighborhood. This study introduces the mode [...] Read more.

The wavelet technique has limitations in detecting damage at the edges of two-dimensional signals. This weakness arises from the nature of the wavelet transform procedure, which shifts the signal by differencing the signal’s pair arrays in the neighborhood. This study introduces the mode shape projection method as an efficient technique for detecting damages in two-dimensional signals in rectangular laminated composite plates to eliminate the weakness of damage detection by the wavelet method. In other words, this paper proposes creating two one-dimensional waves containing information about damages or faults in signals from vibration amplitude signals of composite plates to have an efficient damage detection method. Results show that the proposed method acts much better than wavelet transform and detects damages in numerical and experimental investigations with high performance for various damage scenarios. Full article

(This article belongs to the Special Issue Mathematical and Computational Approaches in Applied Mechanics: A Themed Issue Dedicated to Professor J.N. Reddy)

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20 pages, 6428 KiB

Open AccessArticle

Symbolic Regression for the Determination of Joint Roughness Coefficient

by Yuyang Zhao and Hongbo Zhao

Math. Comput. Appl. 2025, 30(1), 17; https://doi.org/10.3390/mca30010017 - 9 Feb 2025

In this study, a novel symbolic regression-based empirical equation has been developed to compute the joint roughness coefficient (JRC) value based on the statistical parameters of rock joints. The symbolic regression was adopted to map the nonlinear function, which represents the relation between [...] Read more.

In this study, a novel symbolic regression-based empirical equation has been developed to compute the joint roughness coefficient (JRC) value based on the statistical parameters of rock joints. The symbolic regression was adopted to map the nonlinear function, which represents the relation between the JRC and statistical parameters of the rock joint, based on the collected rock joint dataset. It is not necessary to presume the mathematical function form of the empirical equation, which is used to fit the rock joint data while using symbolic regression. The collected rock joint samples from the literature were used to investigate and illustrate the developed symbolic regression-based empirical equation. The performance of the developed empirical equation was compared to the traditional empirical equation. The results show that the generalization performance of the developed empirical equation is better than the traditional empirical equation. They proved that the symbolic regression-based empirical equation characterized the roughness property of rock joints well and that symbolic regression could be used to capture the complex and nonlinear relationship between JRC and the statistical parameters of rock joints. The developed symbolic regression-based empirical equation provides a scientific and excellent tool to estimate the JRC value of rock joints. Full article

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32 pages, 1952 KiB

Open AccessArticle

Stratified Metamodeling to Predict Concrete Compressive Strength Using an Optimized Dual-Layered Architectural Framework

by Geraldo F. Neto, Bruno da S. Macêdo, Tales H. A. Boratto, Tiago Silveira Gontijo, Matteo Bodini, Camila Saporetti and Leonardo Goliatt

Math. Comput. Appl. 2025, 30(1), 16; https://doi.org/10.3390/mca30010016 - 9 Feb 2025

Concrete is one of the most commonly used construction materials worldwide, and its compressive strength is the most important mechanical property to be defined at the time of structural design. Establishing a relationship between the amount of each component in the mixture and [...] Read more.

Concrete is one of the most commonly used construction materials worldwide, and its compressive strength is the most important mechanical property to be defined at the time of structural design. Establishing a relationship between the amount of each component in the mixture and the properties of the concrete is not a trivial task, since a high degree of nonlinearity is involved. However, the use of machine learning methods as modeling tools has assisted in overcoming this difficulty. The objective of this work is to investigate the efficiency of using stacking as a technique for predicting the compressive strength of concrete mixtures. Four datasets obtained from the literature were used to verify the generalization capacity of the stacking technique; these datasets included a number of samples and numbers and types of attributes. Statistical tests were used to compare the existence of significant similarities between stacking and individual machine learning models. The results obtained from the statistical tests and evaluation metrics show that stacking yields results similar to those of the standalone machine learning models, with better performance. Full article

(This article belongs to the Section Engineering)

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29 pages, 1029 KiB

Open AccessArticle

Analysis of a Malaria Transmission Model with Vaccination Proportion and Vaccine-Induced Immunity

by Samuel M. Naandam, Paul Chataa and Gideon K. Gogovi

Math. Comput. Appl. 2025, 30(1), 15; https://doi.org/10.3390/mca30010015 - 4 Feb 2025

This study presents a mathematical model to describe the transmission dynamics of malaria in a highly endemic region, with a focus on vaccination and vaccine-induced immunity as primary control measures. By determining the basic reproduction number (

R_{0}

), we evaluate the [...] Read more.

This study presents a mathematical model to describe the transmission dynamics of malaria in a highly endemic region, with a focus on vaccination and vaccine-induced immunity as primary control measures. By determining the basic reproduction number (

R_{0}

), we evaluate the impact of these interventions on malaria-free and malaria-persistent equilibria. Our analysis shows that the malaria-free equilibrium is locally asymptotically stable when

R_{0} < 1

and unstable otherwise. Numerical simulations demonstrate that increasing vaccination coverage and improving vaccine-induced immunity significantly reduce

R_{0}

. A sensitivity analysis using partial rank correlation coefficients highlights the influence of key parameters, such as the mosquito-to-human transmission rate and mosquito birth and death rates, on malaria transmission. These findings underscore the potential of integrated strategies, combining vaccination with other interventions, to manage malaria effectively in highly endemic regions. Full article

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12 pages, 2873 KiB

Open AccessFeature PaperArticle

Analysis of Primary Healthcare Indicators

by Ana Leonor Saraiva, Cristiana J. Silva, Jorge Cabral, José Pedro Antunes, Paula Rama, Sofia J. Pinheiro and Vera Afreixo

Math. Comput. Appl. 2025, 30(1), 14; https://doi.org/10.3390/mca30010014 - 26 Jan 2025

This study aims to analyze the relationships between various health indicators, using an exploratory graph analysis, repeated measures correlation, and cluster construction. Primary healthcare is essential for providing continuous and comprehensive care, with indicators as crucial tools to identify and improve weaknesses in [...] Read more.

This study aims to analyze the relationships between various health indicators, using an exploratory graph analysis, repeated measures correlation, and cluster construction. Primary healthcare is essential for providing continuous and comprehensive care, with indicators as crucial tools to identify and improve weaknesses in health units. Data from 41 health units in Baixo Vouga, Portugal, from January 2017 to March 2024, were analyzed. Through the database, the behavior of the indicators and health units over time was identified, along with the strongest positive and negative correlations between the indicators and their graphical illustration. Finally, through clusters, the grouping of indicators and health units was achieved. Thus, this study provides healthcare professionals with important insights for the management and continuous improvement of health units. Full article

(This article belongs to the Special Issue New Trends in Biomathematics)

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38 pages, 1875 KiB

Open AccessFeature PaperArticle

Reduced-Order Model for Cell Volume Homeostasis: Application to Aqueous Humor Production

by Riccardo Sacco, Greta Chiaravalli, Giovanna Guidoboni, Anita Layton, Gal Antman, Keren Wood Shalem, Alice Verticchio, Brent Siesky and Alon Harris

Math. Comput. Appl. 2025, 30(1), 13; https://doi.org/10.3390/mca30010013 - 24 Jan 2025

The ability of a cell to keep its volume constant irrespective of intra- and extracellular conditions is essential for cellular homeostasis and survival. The purpose of this study is to elaborate a theoretical model of cell volume homeostasis and to apply it to [...] Read more.

The ability of a cell to keep its volume constant irrespective of intra- and extracellular conditions is essential for cellular homeostasis and survival. The purpose of this study is to elaborate a theoretical model of cell volume homeostasis and to apply it to a simulation of human aqueous humor (AH) production. The model assumes a cell with a spherical shape and only radial deformation satisfying the property that the cell volume in rest conditions equals that of the cell couplets constituting the ciliary epithelium of the human eye. The cytoplasm is described as a homogeneous mixture containing fluid, ions, and neutral solutes whose evolution is determined by net production mechanisms occurring in the intracellular volume and by water and solute exchange across the membrane. Averaging the balance equations over the cell volume leads to a coupled system of nonlinear ordinary differential equations (ODEs) which are solved using the

θ

-method and the Matlab function ode15s. Simulation tests are conducted to characterize the set of parameters corresponding to baseline conditions in AH production. The model is subsequently used to investigate the relative importance of (a) impermeant charged proteins; (b) sodium–potassium (Na+/K+) pumps; (c) carbonic anhydrase (CA) in the AH production process; and (d) intraocular pressure. Results suggest that (a) and (b) play a role; (c) lacks significant weight, at least for low carbon dioxide values; and (d) plays a role for the elevated values of intraocular pressure. Model results describe a higher impact from charged proteins and Na+/K+ ATPase than CA on AH production and cellular volume. The computational virtual laboratory provides a method to further test in vivo experiments and machine learning-based data analysis toward the prevention and cure of ocular diseases such as glaucoma. Full article

(This article belongs to the Special Issue Recent Advances and New Challenges in Coupled Systems and Networks: Theory, Modelling, and Applications)

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22 pages, 1517 KiB

Open AccessArticle

Cyber–Physical System Attack Detection and Isolation: A Takagi–Sugeno Approach

by Angel R. Guadarrama-Estrada, Gloria L. Osorio-Gordillo, Rodolfo A. Vargas-Méndez, Juan Reyes-Reyes and Carlos M. Astorga-Zaragoza

Math. Comput. Appl. 2025, 30(1), 12; https://doi.org/10.3390/mca30010012 - 23 Jan 2025

This paper presents an approach for designing a generalized dynamic observer (GDO) aimed at detecting and isolating attack patterns that compromise the functionality of cyber–physical systems. The considered attack patterns include denial-of-service (DoS), false data injection (FDI), and random data injection (RDI) attacks. [...] Read more.

This paper presents an approach for designing a generalized dynamic observer (GDO) aimed at detecting and isolating attack patterns that compromise the functionality of cyber–physical systems. The considered attack patterns include denial-of-service (DoS), false data injection (FDI), and random data injection (RDI) attacks. To model an attacker’s behavior and enhance the effectiveness of the attack patterns, Markovian logic is employed. The design of the generalized dynamic observer is grounded in the mathematical model of a system, incorporating its dynamics and potential attack scenarios. An attack-to-residual transfer function is utilized to establish the relationship between attack signals and the residuals generated by the observer, enabling effective detection and isolation of various attack schemes. A three-tank interconnected system, modeled under the discrete Takagi–Sugeno representation, is used as a case study to validate the proposed approach. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2024)

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22 pages, 3824 KiB

Open AccessArticle

Rich Dynamics of Seasonal Carrying Capacity Prey-Predator Models with Crowley–Martin Functional Response

by Jawdat Alebraheem

Math. Comput. Appl. 2025, 30(1), 11; https://doi.org/10.3390/mca30010011 - 17 Jan 2025

In this paper, we present novel seasonal carrying capacity prey–predator models with a general functional response, which is that of Crowley–Martin. Seasonality effects are classified into two categories: sudden and periodic perturbations. Models with sudden perturbations are analytically investigated in terms of good [...] Read more.

In this paper, we present novel seasonal carrying capacity prey–predator models with a general functional response, which is that of Crowley–Martin. Seasonality effects are classified into two categories: sudden and periodic perturbations. Models with sudden perturbations are analytically investigated in terms of good and bad circumstances by addressing the existence, positivity, and boundedness of the solution; obtaining the stability conditions for each equilibrium point and the dynamics involving the existence of a limit cycle; determining the Hopf bifurcation with respect to the carrying capacity; and finding the uniform persistence conditions of the models. Moreover, some numerical simulations are performed to demonstrate and validate our theoretical findings. In contrast, models with periodic perturbations are computationally investigated. In analytical findings, the degree of seasonality and the classification of circumstances play a significant role in the uniqueness of the coexistence equilibrium point, the stability of the system, and the existence of a limit cycle. The model with periodic perturbations shows the presence of different dynamics for prey and predator, such as the doubling of the limit cycle and chaos dynamics, so this influence can have a diverse range of possible solutions, which makes the system more enriched with different dynamics. As a result of these findings, many phenomena and changes can be interpreted in ecosystems from an ecological point of view. Full article

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21 pages, 3236 KiB

Open AccessArticle

A Mathematical Approach to the Buckling Problem of Axially Loaded Laminated Nanocomposite Cylindrical Shells in Various Environments

by Abdullah H. Sofiyev, Mahmure Avey and Nigar M. Aslanova

Math. Comput. Appl. 2025, 30(1), 10; https://doi.org/10.3390/mca30010010 - 14 Jan 2025

In this study, the solution of the buckling problem of axially loaded laminated cylindrical shells consisting of functionally graded (FG) nanocomposites in elastic and thermal environments is presented within extended first-order shear deformation theory (FOST) for the first time. The effective material properties [...] Read more.

In this study, the solution of the buckling problem of axially loaded laminated cylindrical shells consisting of functionally graded (FG) nanocomposites in elastic and thermal environments is presented within extended first-order shear deformation theory (FOST) for the first time. The effective material properties and thermal expansion coefficients of nanocomposites in the layers are computed using the extended rule of mixture method and molecular dynamics simulation techniques. The governing relations and equations for laminated cylindrical shells consisting of FG nanocomposites on the two-parameter elastic foundation and in thermal environments are mathematically modeled and solved to find the expression for the axial buckling load. The numerical results of the current analytical approach agree well with the existing literature results obtained using a different methodology. Finally, some new results and interpretations are provided by investigating the influences of different parameters such as elastic foundations, thermal environments, FG nanocomposite models, shear stress, and stacking sequences on the axial buckling load. Full article

(This article belongs to the Special Issue Mathematical and Computational Approaches in Applied Mechanics: A Themed Issue Dedicated to Professor J.N. Reddy)

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15 pages, 626 KiB

Open AccessArticle

Enhanced Forecasting of Equity Fund Returns Using Machine Learning

by Fabiano Fernandes Bargos and Estaner Claro Romão

Math. Comput. Appl. 2025, 30(1), 9; https://doi.org/10.3390/mca30010009 - 13 Jan 2025

This paper aims to explore the integration of machine learning with risk and return performance measures, to provide a data-driven approach to identifying opportunities in equity funds. We built a dataset with 72 performance measures in the columns calculated for multiple periods ranging [...] Read more.

This paper aims to explore the integration of machine learning with risk and return performance measures, to provide a data-driven approach to identifying opportunities in equity funds. We built a dataset with 72 performance measures in the columns calculated for multiple periods ranging from 1 to 120 months. By shifting the values in the 1- and 3-month return columns, we created two new columns, aligning the data for the month t with the return for the month

t + 1

. We categorized each row into one of three classes based on the mean and standard deviation of the shifted 1- and 3-month returns during the period. Based on cross-validated accuracy, we focused on the top three classifiers. As a result, the developed models achieved accuracy, recall, and precision values exceeding 0.92 on the test data. In addition, models trained on 1 year of data maintained predictive reliability for up to 2 months into the future, achieving precision above 90% in forecasting funds with 3-month returns above the average. Thus, this study highlights the effectiveness of machine learning in financial forecasting, particularly within the environment of the Brazilian equity market. Full article

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26 pages, 1448 KiB

Open AccessArticle

Analysis and Optimal Control of Propagation Model for Malware in Multi-Cloud Environments with Impact of Brownian Motion Process

by Othman A. M. Omar, Hamdy M. Ahmed, Taher A. Nofal, Adel Darwish and A. M. Sayed Ahmed

Math. Comput. Appl. 2025, 30(1), 8; https://doi.org/10.3390/mca30010008 - 13 Jan 2025

Today, cloud computing is a widely used technology that provides a wide range of services to numerous sectors around the world. This technology depends on the interaction and cooperation of virtual machines (VMs) to complete various computing tasks, propagating malware attacks quickly due [...] Read more.

Today, cloud computing is a widely used technology that provides a wide range of services to numerous sectors around the world. This technology depends on the interaction and cooperation of virtual machines (VMs) to complete various computing tasks, propagating malware attacks quickly due to the complexity of cloud computing environments and users’ interfaces. As a result of the rising demand for cloud computing from multiple perspectives for complete analysis and decision-making across a range of life disciplines, multi-cloud environments (MCEs) are established. Therefore, in this work, we discuss impacted mathematical modeling for the MCEs’ network dynamics using two deterministic and stochastic approaches. In both approaches, appropriate assumptions are considered. Then, the proposed networks’ VMs are classified to have six different possible states covering media, healthcare, finance, and educational servers. After that, the two developed modeling approaches’ solution existence, uniqueness, equilibrium, and stability are carefully investigated. Using an optimal control strategy, both proposed models are tested for sustaining a certain level of security of the VMs’ states and reducing the propagation of malware within the networks. Finally, we verify the theoretical results by employing numerical simulations to track the malware’s propagation immunization. Results showed how the implemented control methods maintained the essential objectives of managing malware infections. Full article

(This article belongs to the Special Issue Recent Advances and New Challenges in Coupled Systems and Networks: Theory, Modelling, and Applications)

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13 pages, 1838 KiB

Open AccessArticle

Application of Generalized Finite Difference Method and Radial Basis Function Neural Networks in Solving Inverse Problems of Surface Anomalous Diffusion

by Luchuan Shi and Qiang Xi

Math. Comput. Appl. 2025, 30(1), 7; https://doi.org/10.3390/mca30010007 - 9 Jan 2025

In this study, a new hybrid method based on the generalized finite difference method (GFDM) and radial basis function (RBF) neural network technologies is developed to solve the inverse problems of surface anomalous diffusion. Specifically, the GFDM is utilized to compute the time-fractional [...] Read more.

In this study, a new hybrid method based on the generalized finite difference method (GFDM) and radial basis function (RBF) neural network technologies is developed to solve the inverse problems of surface anomalous diffusion. Specifically, the GFDM is utilized to compute the time-fractional derivative model on the surface, whereas RBF neural networks are employed to invert the diffusion coefficient, source term coefficient, and the fractional order within the anomalous diffusion equation governing the surface. The results of four examples show that for the three parameters of diffusion coefficient, source term coefficient, and fractional order, the errors of inversion results are in the order of

1 0^{- 2}

under different conditions. Therefore, this method can obtain the required parameters quickly and accurately under different conditions. Full article

(This article belongs to the Special Issue Radial Basis Functions)

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21 pages, 5013 KiB

Open AccessArticle

A New Fractional Boundary Element Model for the 3D Thermal Stress Wave Propagation Problems in Anisotropic Materials

by Mohamed Abdelsabour Fahmy and Moncef Toujani

Math. Comput. Appl. 2025, 30(1), 6; https://doi.org/10.3390/mca30010006 - 8 Jan 2025

The primary purpose of this work is to provide a new fractional boundary element method (BEM) formulation to solve thermal stress wave propagation problems in anisotropic materials. In the Laplace domain, the fundamental solutions to the governing equations can be identified. Then, the [...] Read more.

The primary purpose of this work is to provide a new fractional boundary element method (BEM) formulation to solve thermal stress wave propagation problems in anisotropic materials. In the Laplace domain, the fundamental solutions to the governing equations can be identified. Then, the boundary integral equations are constructed. The Caputo fractional time derivative was used in the formulation of the considered heat conduction equation. The three-block splitting (TBS) iteration approach was used to solve the resulting BEM linear systems, resulting in fewer iterations and less CPU time. The new TBS iteration method converges rapidly and does not involve complicated computations; it performs better than the two-dimensional double successive projection method (2D-DSPM) and modified symmetric successive overrelaxation (MSSOR) for solving the resultant BEM linear system. We only studied a special case of our model to compare our findings to those of other articles in the literature. Because the BEM results are so consistent with the finite element method (FEM) findings, the numerical results demonstrate the validity, accuracy, and efficiency of our proposed BEM formulation for solving three-dimensional thermal stress wave propagation problems in anisotropic materials. Full article

(This article belongs to the Special Issue Mathematical and Computational Approaches in Applied Mechanics: A Themed Issue Dedicated to Professor J.N. Reddy)

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12 pages, 4409 KiB

Open AccessArticle

Forced Vibration Behaviour of Elastically Constrained Graphene Origami-Enabled Auxetic Metamaterial Beams

by Behrouz Karami and Mergen H. Ghayesh

Math. Comput. Appl. 2025, 30(1), 5; https://doi.org/10.3390/mca30010005 - 7 Jan 2025

This paper explores the vibration behaviour of an elastically constrained graphene origami-enabled auxetic metamaterial beam subject to a harmonic external force. The effective mechanical properties of the metamaterial are approximated using a micromechanical model trained via a genetic algorithm provided in the literature. [...] Read more.

This paper explores the vibration behaviour of an elastically constrained graphene origami-enabled auxetic metamaterial beam subject to a harmonic external force. The effective mechanical properties of the metamaterial are approximated using a micromechanical model trained via a genetic algorithm provided in the literature. The three coupled equations of motion are solved numerically; a set of trigonometric functions is used to approximate the displacement components. The accuracy of the proposed model is confirmed by comparing it with the natural frequencies of a simplified non-metamaterial structure available in the literature. Following this validation, the investigation extends to investigate the forced vibration response of the metamaterial beam, examining the influence of the graphene origami distribution pattern and content, graphene folding degree, linear and shear layer stiffness, and geometrical parameters on the dynamic behaviour of the structure. The results generally highlight the considerable effect of the shear layer, modelled as a Pasternak foundation, on the vibration behaviour of the elastically constrained metamaterial beams. Full article

(This article belongs to the Special Issue Mathematical and Computational Approaches in Applied Mechanics: A Themed Issue Dedicated to Professor J.N. Reddy)

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24 pages, 734 KiB

Open AccessArticle

Economic Peaks and Value-at-Risk Analysis: A Novel Approach Using the Laplace Distribution for House Prices

by Jondeep Das, Partha Jyoti Hazarika, Morad Alizadeh, Javier E. Contreras-Reyes, Hebatallah H. Mohammad and Haitham M. Yousof

Math. Comput. Appl. 2025, 30(1), 4; https://doi.org/10.3390/mca30010004 - 7 Jan 2025

In this article, a new extension of the standard Laplace distribution is introduced for house price modeling. Certain important properties of the new distribution are deducted throughout this study. We used the new extension of the Laplace model to conduct a thorough economic [...] Read more.

In this article, a new extension of the standard Laplace distribution is introduced for house price modeling. Certain important properties of the new distribution are deducted throughout this study. We used the new extension of the Laplace model to conduct a thorough economic risk assessment utilizing several metrics, including the value-at-risk (VaR), the peaks over a random threshold value-at-risk (PORT-VaR), the tail value-at-risk (TVaR), the mean of order-P (MO^P), and the peaks over a random threshold based on the mean of order-P (PORT-MO^P). These metrics capture different facets of the tail behavior, which is essential for comprehending the extreme median values in the Boston house price data. Notably, PORT-VaR improves the risk evaluations by incorporating randomness into the selection of the thresholds, whereas VaR and TVaR focus on measuring the potential losses at specific confidence levels, with TVaR offering insights into significant tail risks. The MO^P method aids in balancing the reliability goals while optimizing the performance in the face of uncertainty. Full article

(This article belongs to the Section Social Sciences)

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16 pages, 739 KiB

Open AccessArticle

High-Order Finite Difference Hermite Weighted Essentially Nonoscillatory Method for Convection–Diffusion Equations

by Yabo Wang and Hongxia Liu

Math. Comput. Appl. 2025, 30(1), 3; https://doi.org/10.3390/mca30010003 - 3 Jan 2025

A kind of finite difference Hermite WENO (HWENO) method is presented in this paper to deal with convection-dominated convection-diffusion equations in uniform grids. The benefit of the HWENO method is its compactness, allowing great accuracy to be attained in the solution’s smooth regions [...] Read more.

A kind of finite difference Hermite WENO (HWENO) method is presented in this paper to deal with convection-dominated convection-diffusion equations in uniform grids. The benefit of the HWENO method is its compactness, allowing great accuracy to be attained in the solution’s smooth regions and maintaining the essential nonoscillation in the solution’s discontinuities. We discretize the convection term using the HWENO method and the diffusion term using the Hermite central interpolation schemes. However, it is difficult to deal with mixed derivative terms when solving two-dimensional problems using the HWENO method mentioned. To address this problem, we also employ the Hermite interpolation approach, which can keep the compactness. Lastly, we apply this method to two-dimensional Navier-Stokes problems that are incompressible. The efficiency and stability of the presented method are illustrated through numerous numerical experiments. Full article

(This article belongs to the Topic Numerical Methods for Partial Differential Equations)

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24 pages, 6897 KiB

Open AccessArticle

Data-Driven Fault Diagnosis in Water Pipelines Based on Neuro-Fuzzy Zonotopic Kalman Filters

by Esvan-Jesús Pérez-Pérez, Yair González-Baldizón, José-Armando Fragoso-Mandujano, Julio-Alberto Guzmán-Rabasa and Ildeberto Santos-Ruiz

Math. Comput. Appl. 2025, 30(1), 2; https://doi.org/10.3390/mca30010002 - 30 Dec 2024

This work presents a data-driven approach for diagnosing sensor faults and leaks in hydraulic pipelines using neuro-fuzzy Zonotopic Kalman Filters (ZKF). The approach involves two key steps: first, identifying the nonlinear pipeline system using an adaptive neuro-fuzzy inference system (ANFIS), resulting in a [...] Read more.

This work presents a data-driven approach for diagnosing sensor faults and leaks in hydraulic pipelines using neuro-fuzzy Zonotopic Kalman Filters (ZKF). The approach involves two key steps: first, identifying the nonlinear pipeline system using an adaptive neuro-fuzzy inference system (ANFIS), resulting in a set of Takagi–Sugeno fuzzy models derived from pressure and flow data, and second, implementing a neuro-fuzzy ZKF bench to detect pipeline leaks and sensor faults with adaptive thresholds. The learning phase of the neuro-fuzzy systems considers only fault-free data. Fault isolation is achieved by comparing zonotopic sets and evaluating a fault signature matrix. The method accounts for parametric uncertainty and measurement noise, ensuring robustness. Experimental validation on a hydraulic pipeline demonstrated high precision (up to 99.24%), recall (up to 99.20%), and low false positive rates (as low as 0.76%) across various fault scenarios and operational points. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2024)

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