Mathematical and Computational Applications

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

Abstract

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

Abstract

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

Abstract

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

Abstract

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

Abstract

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

Abstract

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

Abstract

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

Abstract

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

Abstract

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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26 pages, 5504 KiB

Open AccessArticle

Advanced Hybrid Brain Tumor Segmentation in MRI: Elephant Herding Optimization Combined with Entropy-Guided Fuzzy Clustering

by Baiju Karun, Arunprasath Thiyagarajan, Pallikonda Rajasekaran Murugan, Natarajan Jeyaprakash, Kottaimalai Ramaraj and Rakhee Makreri

Math. Comput. Appl. 2025, 30(1), 1; https://doi.org/10.3390/mca30010001 - 25 Dec 2024

Abstract

Accurate and early detection of brain tumors is essential for improving clinical outcomes and guiding effective treatment planning. Traditional segmentation techniques in MRI often struggle with challenges such as noise, intensity variations, and complex tumor morphologies, which can hinder their effectiveness in critical [...] Read more.

Accurate and early detection of brain tumors is essential for improving clinical outcomes and guiding effective treatment planning. Traditional segmentation techniques in MRI often struggle with challenges such as noise, intensity variations, and complex tumor morphologies, which can hinder their effectiveness in critical healthcare scenarios. This study proposes an innovative hybrid methodology that integrates advanced metaheuristic optimization and entropy-based fuzzy clustering to enhance segmentation precision in brain tumor detection. This method combines the nature-inspired Elephant Herding Optimization (EHO) algorithm with Entropy-Driven Fuzzy C-Means (EnFCM) clustering, offering significant improvements over conventional methods. EHO is utilized to optimize the clustering process, enhancing the algorithm’s ability to delineate tumor boundaries, while entropy-based fuzzy clustering accounts for intensity inhomogeneity and diverse tumor characteristics, promoting more consistent and reliable segmentation results. This approach was evaluated using the BraTS challenge dataset, a benchmark in the field of brain tumor segmentation. The results demonstrate marked improvements across several performance metrics, including Dice similarity, mean squared error (MSE), peak signal-to-noise ratio (PSNR), and the Tanimoto coefficient (TC), underscoring this method’s robustness and segmentation accuracy. By managing image noise and reducing computational demands, the EHO-EnFCM approach not only captures intricate tumor structures but also facilitates efficient image processing, making it suitable for real-time clinical applications. Overall, the findings reveal the potential of this hybrid approach to advance MRI-based tumor detection, offering a promising tool that enhances both accuracy and computational efficiency for medical imaging and diagnosis. Full article

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15 pages, 752 KiB

Open AccessArticle

Classification of Red Blood Cells in the Kendall Space of Reflection Shapes

by Ximo Gual-Arnau and Lluïsa Gual-Vayà

Math. Comput. Appl. 2024, 29(6), 122; https://doi.org/10.3390/mca29060122 - 19 Dec 2024

Abstract

The classification of red blood cells (RBCs) or erythrocytes into three categories based on their shape, normal, sickle-shaped, and those with other deformations, has proven to be a crucial tool in diagnosing and managing sickle cell disease (SCD). Manual classification techniques have evolved [...] Read more.

The classification of red blood cells (RBCs) or erythrocytes into three categories based on their shape, normal, sickle-shaped, and those with other deformations, has proven to be a crucial tool in diagnosing and managing sickle cell disease (SCD). Manual classification techniques have evolved into automated tools, with numerous classification methods being applied based on different ways of representing the cells. In this work, we propose a novel methodology for representing RBCs, defined by selecting k landmarks along the cell boundaries and characterizing shapes as points in the Kendall space of reflection shapes,

Ω_{2}^{k}

. Using this representation, we applied an embedding of the Kendall space

Ω_{2}^{k}

into a Euclidean space, which allowed for the use of machine learning classification algorithms. We also compared our results with those obtained using other classification methods applied to the same dataset in the literature, highlighting the strong performance of our approach in terms of classification accuracy. Full article

(This article belongs to the Section Natural Sciences)

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13 pages, 1235 KiB

Open AccessArticle

Features of Generation, Propagation and Application of Special Ultrasonic Impulses in Viscous Liquids

by Oleg M. Gradov

Math. Comput. Appl. 2024, 29(6), 121; https://doi.org/10.3390/mca29060121 - 18 Dec 2024

Abstract

An exact numerical and approximate analytical description of solitary acoustic pulses with a large difference in spatial gradients of parameters in different directions has been obtained in viscous liquids using this small parameter. The method of special initial-boundary conditions obtained during analyzing the [...] Read more.

An exact numerical and approximate analytical description of solitary acoustic pulses with a large difference in spatial gradients of parameters in different directions has been obtained in viscous liquids using this small parameter. The method of special initial-boundary conditions obtained during analyzing the hydrodynamic equations has been applied to describe the peculiarities of this nonlinear phenomenon. Waves of this type exist in the presence of two- or three-dimensional inhomogeneity of the initial disturbances and retain a spatial structure along the direction of propagation when traveling long distances. At the same time, it is possible to regulate the pressure drop and the speed of the acoustic signal, which creates unique conditions for a special force effect or information transmission. The efficiency of their use in such processes as metal dissolution, solvent extraction and mass transfer under the conditions of resonance exposure of ultrasound was evaluated. Fine details of exciting the nonlinear impulse with the necessary properties have been analyzed to demonstrate a possible way to a new technology of successfully treating any different specimens, materials and constructions for a long distance between the source of radiation and the position of the treatment. The use of such pulses opens up new opportunities for remote acoustic force impact on various objects, as well as for the transmission of information. Full article

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18 pages, 502 KiB

Open AccessArticle

Efficient Finite-Difference Estimation of Second-Order Parametric Sensitivities for Stochastic Discrete Biochemical Systems

by Fauzia Jabeen and Silvana Ilie

Math. Comput. Appl. 2024, 29(6), 120; https://doi.org/10.3390/mca29060120 - 17 Dec 2024

Abstract

Biochemical reaction systems in a cell exhibit stochastic behaviour, owing to the unpredictable nature of the molecular interactions. The fluctuations at the molecular level may lead to a different behaviour than that predicted by the deterministic model of the reaction rate equations, when [...] Read more.

Biochemical reaction systems in a cell exhibit stochastic behaviour, owing to the unpredictable nature of the molecular interactions. The fluctuations at the molecular level may lead to a different behaviour than that predicted by the deterministic model of the reaction rate equations, when some reacting species have low population numbers. As a result, stochastic models are vital to accurately describe system dynamics. Sensitivity analysis is an important method for studying the influence of the variations in various parameters on the output of a biochemical model. We propose a finite-difference strategy for approximating second-order parametric sensitivities for stochastic discrete models of biochemically reacting systems. This strategy utilizes adaptive tau-leaping schemes and coupling of the perturbed and nominal processes for an efficient sensitivity estimation. The advantages of the new technique are demonstrated through its application to several biochemical system models with practical significance. 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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16 pages, 569 KiB

Open AccessArticle

New Metaheuristics to Solve the Internet Shopping Optimization Problem with Sensitive Prices

by Miguel A. García-Morales, José Alfredo Brambila-Hernández, Héctor J. Fraire-Huacuja, Juan Frausto, Laura Cruz, Claudia Gómez and Alfredo Peña-Ramos

Math. Comput. Appl. 2024, 29(6), 119; https://doi.org/10.3390/mca29060119 - 14 Dec 2024

Abstract

In this research, two new methods for solving the Internet shopping optimization problem with sensitive prices are proposed, incorporating adaptive adjustment of control parameters. This problem is classified as NP-hard and is relevant to current electronic commerce. The first proposed solution method corresponds [...] Read more.

In this research, two new methods for solving the Internet shopping optimization problem with sensitive prices are proposed, incorporating adaptive adjustment of control parameters. This problem is classified as NP-hard and is relevant to current electronic commerce. The first proposed solution method corresponds to a Memetic Algorithm incorporating improved local search and adaptive adjustment of control parameters. The second proposed solution method is a particle swarm optimization algorithm that adds a technique for diversification and adaptive adjustment of control parameters. We assess the effectiveness of the proposed algorithms by comparing them with the Branch and Bound algorithm, which presents the most favorable outcomes of the state-of-the-art method. Nine instances of three different sizes are used: small, medium, and large. For performance validation, the Wilcoxon and Friedman non-parametric tests are applied. The results show that the proposed algorithms exhibit comparable performance and outperform the Branch and Bound algorithm. Full article

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

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28 pages, 2994 KiB

Open AccessArticle

Design of Dual-Channel Supply Chain Network Based on the Internet of Things Under Uncertainty

by Hamed Nozari, Hossein Abdi, Agnieszka Szmelter-Jarosz and Seyyed Hesamoddin Motevalli

Math. Comput. Appl. 2024, 29(6), 118; https://doi.org/10.3390/mca29060118 - 12 Dec 2024

Abstract

In this paper, a mathematical model of a dual-channel supply chain network (DCSCN) based on the Internet of Things (IoT) under uncertainty is presented, and its solution using algorithms based on artificial intelligence such as genetic algorithm (GA), particle swarm optimization (PSO), imperialist [...] Read more.

In this paper, a mathematical model of a dual-channel supply chain network (DCSCN) based on the Internet of Things (IoT) under uncertainty is presented, and its solution using algorithms based on artificial intelligence such as genetic algorithm (GA), particle swarm optimization (PSO), imperialist competitive algorithm (ICA), and gray wolf optimizer (GWO). The main goal of this model is to maximize the total DCSCN profit to determine the amount of demand accurately, price in direct and indirect channels, locate distribution centers, and equip/not equip these centers with IoT devices. The results show that with the increase in the uncertainty rate, the amount of demand and corresponding transportation costs have increased. This issue has led to a decrease in the total DCSCN profit. By analyzing the mathematical model, it was also observed that deploying IoT equipment in distribution centers has increased fixed costs. Examining this issue shows that by increasing the savings factor by 0.2, the total DCSCN profit has increased by 6.5%. By ranking the algorithms with the TOPSIS method, the GA was ranked as the most efficient algorithm, followed by PSO, ICA, and GWO. This IoT-enhanced dual-channel supply chain model not only aims to optimize traditional supply chain metrics but also introduces advanced, data-driven strategies for improving demand management, pricing, and infrastructure allocation, ultimately driving profitability in uncertain environments. Full article

(This article belongs to the Special Issue Computational Approaches and Data Analysis in the Smart Supply Chain, with an Emphasis on AI, IoT and Big Data)

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29 pages, 6603 KiB

Open AccessArticle

A Mathematical Study of Effects of Alzheimer’s Drug Donepezil Hydrochloride on Neuronal Viscoelasticity and Action Potentials

by Corina S. Drapaca

Math. Comput. Appl. 2024, 29(6), 117; https://doi.org/10.3390/mca29060117 - 12 Dec 2024

Abstract

Alzheimer’s disease (AD) is a degenerative disorder characterized by progressive cognitive decline and memory loss. The few contemporary therapies may ease symptoms and/or slow down AD progression but cannot cure the disease. The orally administered AD drug donepezil hydrochloride enhances the availability of [...] Read more.

Alzheimer’s disease (AD) is a degenerative disorder characterized by progressive cognitive decline and memory loss. The few contemporary therapies may ease symptoms and/or slow down AD progression but cannot cure the disease. The orally administered AD drug donepezil hydrochloride enhances the availability of acetylcholine that supports cholinergic neurotransmission. In this paper, a generalized Hodgkin-Huxley model is proposed that uses Caputo fractional order temporal derivatives to link action potentials and viscoelasticity of cholinergic receptors. The model provides not only structurally dependent action potentials for health and AD but also a possible mechanism of donepezil effect on action potentials: the binding between the acetylcholine and the receptors preserves the structural fitness of these receptors. In addition, a generalized pharmacokinetic model of donepezil transport to the brain is proposed that incorporates controlled release modalities. Caputo fractional order temporal derivatives are used again to model anomalous drug release. Numerical simulations show how controlled release donepezil recovers the structural integrity of the receptors which further brings the abnormal action potentials due to AD to their healthy state. The results suggest that combining various drug release modalities and dosages may improve treatment effectiveness with donepezil. 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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23 pages, 3275 KiB

Open AccessArticle

A PDE-ODE Coupled Model for Biofilm Growth in Porous Media That Accounts for Longitudinal Diffusion and Its Effect on Substrate Degradation

by Emma Bottomley and Hermann J. Eberl

Math. Comput. Appl. 2024, 29(6), 116; https://doi.org/10.3390/mca29060116 - 11 Dec 2024

Abstract

We derive a one-dimensional macroscopic model for biofilm formation in a porous medium reactor to investigate the role of longitudinal diffusion of substrate and suspended bacteria on reactor performance. By comparing an existing base model—one without longitudinal diffusion, which was the point of [...] Read more.

We derive a one-dimensional macroscopic model for biofilm formation in a porous medium reactor to investigate the role of longitudinal diffusion of substrate and suspended bacteria on reactor performance. By comparing an existing base model—one without longitudinal diffusion, which was the point of departure for our work, to the new model—we noticed significant changes in system dynamics. Our results suggest that neglecting it can lead to underestimation of quenching length and biofilm accumulation downstream, even in the advection-dominated regime. The effects of attachment and detachment of suspended bacteria on biofilm formation and substrate degradation were also examined. In the one-dimensional model, it was found that attachment has a stronger influence on substrate depletion, which becomes more pronounced as diffusion in the pore space increases. Full article

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

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12 pages, 3814 KiB

Open AccessArticle

Compressive Sensing of Multichannel Electroencephalogram Signals Based on Nonlocal Low-Rank and Cosparse Priors

by Jun Zhu, Lei Feng and Chunmeng Wang

Math. Comput. Appl. 2024, 29(6), 115; https://doi.org/10.3390/mca29060115 - 6 Dec 2024

Abstract

Recent studies have shown that by using channel-correlation and cosparsity in a centralized framework, the accuracy of reconstructing multichannel EEG signals can be improved. A single-channel electroencephalogram (EEG) signal is intrinsically non-sparse in both the converted and raw time domains, which presents a [...] Read more.

Recent studies have shown that by using channel-correlation and cosparsity in a centralized framework, the accuracy of reconstructing multichannel EEG signals can be improved. A single-channel electroencephalogram (EEG) signal is intrinsically non-sparse in both the converted and raw time domains, which presents a number of important issues. However, this is ignored by contemporary compressive sensing (CS) algorithms, resulting in less recovery quality than is ideal. To address these constraints, we provide a novel CS method that takes advantage of Nonlocal Low-Rank and Cosparse priors (NLRC). By utilizing low-rank approximations and block operations, our method aims to improve the CS recovery process and take advantage of channel correlations. The Alternating Direction Method of Multipliers (ADMM) are also used to efficiently solve the resulting non-convex optimization problem. The outcomes of the experiments unequivocally demonstrate that by using NLRC, the quality of signal reconstruction is significantly enhanced. Full article

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22 pages, 2331 KiB

Open AccessArticle

A Novel Hybrid Computational Technique to Study Conformable Burgers’ Equation

by Abdul-Majeed Ayebire, Atul Pasrija, Mukhdeep Singh Manshahia and Shelly Arora

Math. Comput. Appl. 2024, 29(6), 114; https://doi.org/10.3390/mca29060114 - 5 Dec 2024

Abstract

A fully discrete computational technique involving the implicit finite difference technique and cubic Hermite splines is proposed to solve the non-linear conformable damped Burgers’ equation with variable coefficients numerically. The proposed scheme is capable of solving the equation having singularity at [...] Read more.

A fully discrete computational technique involving the implicit finite difference technique and cubic Hermite splines is proposed to solve the non-linear conformable damped Burgers’ equation with variable coefficients numerically. The proposed scheme is capable of solving the equation having singularity at

t = 0

. The space direction is discretized using cubic Hermite splines, whereas the time direction is discretized using an implicit finite difference scheme. The convergence, stability and error estimates of the proposed scheme are discussed in detail to prove the efficiency of the technique. The convergence of the proposed scheme is found to be of order

h^{2}

in space and order

{(Δ t)}^{α}

in the time direction. The efficiency of the proposed scheme is verified by calculating error norms in the Eucledian and supremum sense. The proposed technique is applied on conformable damped Burgers’ equation with different initial and boundary conditions and the results are presented as tables and graphs. Comparison with results already in the literature also validates the application of the proposed technique. Full article

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

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