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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 28.8 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 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

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

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

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

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

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

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

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

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

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

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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18 pages, 1079 KiB

Open AccessFeature PaperArticle

A Network-Based Study of the Dynamics of Aβ and τ Proteins in Alzheimer’s Disease

by Stefano Bianchi, Germana Landi, Camilla Marella, Maria Carla Tesi, Claudia Testa and on behalf of the Alzheimer’s Disease Neuroimaging Initiative

Math. Comput. Appl. 2024, 29(6), 113; https://doi.org/10.3390/mca29060113 - 4 Dec 2024

Due to the extreme complexity of Alzheimer’s disease (AD), the etiology of which is not yet known, and for which there are no known effective treatments, mathematical modeling can be very useful. Indeed, mathematical models, if deemed reliable, can be used to test [...] Read more.

Due to the extreme complexity of Alzheimer’s disease (AD), the etiology of which is not yet known, and for which there are no known effective treatments, mathematical modeling can be very useful. Indeed, mathematical models, if deemed reliable, can be used to test medical hypotheses that could be difficult to verify directly. In this context, it is important to understand how

A β

and

τ

proteins, which, in abnormal aggregate conformations, are hallmarks of the disease, interact and spread. We are particularly interested, in this paper, in studying the spreading of misfolded

τ

. To this end, we present four different mathematical models, all on networks on which the protein evolves. The models differ in both the choice of network and diffusion operator. Through comparison with clinical data on

τ

concentration, which we carefully obtained with multimodal analysis techniques, we show that some models are more adequate than others to simulate the dynamics of the protein. This type of study may suggest that, when it comes to modeling certain pathologies, the choice of the mathematical setting must be made with great care if comparison with clinical data is considered decisive. 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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Graphical abstract

28 pages, 995 KiB

Open AccessFeature PaperArticle

A Conservative and Compact Finite Difference Scheme for the Sixth-Order Boussinesq Equation with Surface Tension

by Xiaofeng Wang, Weizhong Dai and Anjan Biswas

Math. Comput. Appl. 2024, 29(6), 112; https://doi.org/10.3390/mca29060112 - 29 Nov 2024

In this study, we propose a conservative and compact finite difference scheme designed to preserve both the mass change rate and energy for solving the sixth-order Boussinesq equation with surface tension. Theoretical analysis confirms that the proposed scheme achieves second-order accuracy in temporal [...] Read more.

In this study, we propose a conservative and compact finite difference scheme designed to preserve both the mass change rate and energy for solving the sixth-order Boussinesq equation with surface tension. Theoretical analysis confirms that the proposed scheme achieves second-order accuracy in temporal discretization and fourth-order accuracy in spatial discretization. The solvability, convergence, and stability of the difference scheme are rigorously established through the application of the discrete energy method. Additionally, a series of numerical experiments are conducted to illustrate the effectiveness and reliability of the conservative scheme for long-time simulations. 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, 2920 KiB

Open AccessArticle

Dynamic Time Warping as Elementary Effects Metric for Morris-Based Global Sensitivity Analysis of High-Dimension Dynamical Models

by Dhan Lord B. Fortela, Ashley P. Mikolajczyk, Rafael Hernandez, Emmanuel Revellame, Wayne Sharp, William Holmes, Daniel Gang and Mark E. Zappi

Math. Comput. Appl. 2024, 29(6), 111; https://doi.org/10.3390/mca29060111 - 27 Nov 2024

This work focused on demonstrating the use of dynamic time warping (DTW) as a metric for the elementary effects computation in Morris-based global sensitivity analysis (GSA) of model parameters in multivariate dynamical systems. One of the challenges of GSA on multivariate time-dependent dynamics [...] Read more.

This work focused on demonstrating the use of dynamic time warping (DTW) as a metric for the elementary effects computation in Morris-based global sensitivity analysis (GSA) of model parameters in multivariate dynamical systems. One of the challenges of GSA on multivariate time-dependent dynamics is the modeling of parameter perturbation effects propagated to all model outputs while capturing time-dependent patterns. The study establishes and demonstrates the use of DTW as a metric of elementary effects across the time domain and the multivariate output domain, which are all aggregated together via the DTW cost function into a single metric value. Unlike the commonly studied coefficient-based functional approximation and covariance decomposition methods, this new DTW-based Morris GSA algorithm implements curve alignment via dynamic programing for cost computation in every parameter perturbation trajectory, which captures the essence of “elementary effect” in the original Morris formulation. This new algorithm eliminates approximations and assumptions about the model outputs while achieving the objective of capturing perturbations across time and the array of model outputs. The technique was demonstrated using an ordinary differential equation (ODE) system of mixed-order adsorption kinetics, Monod-type microbial kinetics, and the Lorenz attractor for chaotic solutions. DTW as a Morris-based GSA metric enables the modeling of parameter sensitivity effects on the entire array of model output variables evolving in the time domain, resulting in parameter rankings attributed to the entire model dynamics. Full article

(This article belongs to the Special Issue Numerical and Symbolic Computation: Developments and Applications 2025)

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Graphical abstract

21 pages, 5633 KiB

Open AccessArticle

Polynomial Approximation over Arbitrary Shape Domains

by Mohammad J. Mahtabi, Arash Ghasemi, Amirehsan Ghasemi and James C. Newman III

Math. Comput. Appl. 2024, 29(6), 110; https://doi.org/10.3390/mca29060110 - 25 Nov 2024

In spectral/finite element methods, a robust and stable high-order polynomial approximation method for the solution can significantly reduce the required number of degrees of freedom (DOFs) to achieve a certain level of accuracy. In this work, a closed-form relation is proposed to approximate [...] Read more.

In spectral/finite element methods, a robust and stable high-order polynomial approximation method for the solution can significantly reduce the required number of degrees of freedom (DOFs) to achieve a certain level of accuracy. In this work, a closed-form relation is proposed to approximate the Fekete points (AFPs) on arbitrary shape domains based on the singular value decomposition (SVD) of the Vandermonde matrix. In addition, a novel method is derived to compute the moments on highly complex domains, which may include discontinuities. Then, AFPs are used to generate compatible basis functions using SVD. Equations are derived and presented to determine orthogonal/orthonormal modal basis functions, as well as the Lagrange basis. Furthermore, theorems are proved to show the convergence and accuracy of the proposed method, together with an explicit form of the Weierstrass theorem for polynomial approximation. The method was implemented and some classical cases were analyzed. The results show the superior performance of the proposed method in terms of convergence and accuracy using many fewer DOFs and, thus, a much lower computational cost. It was shown that the orthogonal modal basis is the best choice to decrease the DOFs while maintaining a small Lebesgue constant when very high degree of polynomial is employed. 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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3 pages, 194 KiB

Open AccessEditorial

Mathematical and Computational Modelling in Mechanics of Materials and Structures

by Nicholas Fantuzzi, Francesco Fabbrocino, Marco Montemurro, Francesca Nanni, Qun Huang, José António Correia, Leonardo Dassatti and Michele Bacciocchi

Math. Comput. Appl. 2024, 29(6), 109; https://doi.org/10.3390/mca29060109 - 25 Nov 2024

The intersection of mathematics and computational modeling with the mechanics of materials and structural engineering continues to yield substantial advancements in both theoretical and applied domains [...] Full article

(This article belongs to the Special Issue Mathematical and Computational Modelling in Mechanics of Materials and Structures)

25 pages, 1607 KiB

Open AccessReview

Optimizing Power Flow and Stability in Hybrid AC/DC Microgrids: AC, DC, and Combined Analysis

by Ghanshyam Meena, Veerpratap Meena, Akhilesh Mathur, Vinay Pratap Singh, Ahmad Taher Azar and Ibrahim A. Hameed

Math. Comput. Appl. 2024, 29(6), 108; https://doi.org/10.3390/mca29060108 - 24 Nov 2024

A microgrid (MG) is a unique area of a power distribution network that combines distributed generators (conventional as well as renewable power sources) and energy storage systems. Due to the integration of renewable generation sources, microgrids have become more unpredictable. MGs can operate [...] Read more.

A microgrid (MG) is a unique area of a power distribution network that combines distributed generators (conventional as well as renewable power sources) and energy storage systems. Due to the integration of renewable generation sources, microgrids have become more unpredictable. MGs can operate in two different modes, namely, grid-connected and islanded modes. MGs face various challenges of voltage variations, frequency deviations, harmonics, unbalances, etc., due to the uncertain behavior of renewable sources. To study the impact of these issues, it is necessary to analyze the behavior of the MG system under normal and abnormal operating conditions. Two different tools are used for the analysis of microgrids under normal and abnormal conditions, namely, power flow and short-circuit analysis, respectively. Power flow analysis is used to determine the voltages, currents, and real and reactive power flow in the MG system under normal operating conditions. Short-circuit analysis is carried out to analyze the behavior of MGs under faulty conditions. In this paper, a review of power flow and short-circuit analysis algorithms for MG systems under two different modes of operation, grid-connected and islanded, is presented. This paper also presents a comparison of various power flow as well as short-circuit analysis techniques for MGs in tabular form. The modeling of different components of MGs is also discussed in this paper. Full article

(This article belongs to the Special Issue Applied Optimization in Automatic Control and Systems Engineering)

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18 pages, 2638 KiB

Open AccessArticle

Radical Petrov–Galerkin Approach for the Time-Fractional KdV–Burgers’ Equation

by Youssri Hassan Youssri and Ahmed Gamal Atta

Math. Comput. Appl. 2024, 29(6), 107; https://doi.org/10.3390/mca29060107 - 21 Nov 2024

This paper presents a novel numerical spectral scheme to handle the time-fractional KdV–Burgers’ equation, which is very important in both physics and engineering. The scheme basically uses the tau approach combined with Gegenbauer polynomials to provide accurate and stable numerical solutions. Instead of [...] Read more.

This paper presents a novel numerical spectral scheme to handle the time-fractional KdV–Burgers’ equation, which is very important in both physics and engineering. The scheme basically uses the tau approach combined with Gegenbauer polynomials to provide accurate and stable numerical solutions. Instead of solving the differential problem together with the conditions, we solve a system of algebraic equations. The method can handle complex boundary conditions. Some numerical experiments are exhibited to demonstrate that this approach is highly efficient and produces results that are better than some existing numerical methods in the literature. This technique offers more advanced solutions for time-fractional problems in various fields. Full article

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23 pages, 463 KiB

Open AccessArticle

Semantic Categories: Uncertainty and Similarity

by Ares Fabregat-Hernández, Javier Palanca and Vicent Botti

Math. Comput. Appl. 2024, 29(6), 106; https://doi.org/10.3390/mca29060106 - 16 Nov 2024

This paper addresses understanding and categorizing language by using Markov categories to establish a mathematical framework for semantic concepts. This framework enables us to measure the semantic similarity between linguistic expressions within a given text. Furthermore, this approach enables the measurement and control [...] Read more.

This paper addresses understanding and categorizing language by using Markov categories to establish a mathematical framework for semantic concepts. This framework enables us to measure the semantic similarity between linguistic expressions within a given text. Furthermore, this approach enables the measurement and control of uncertainty in language categorization and the creation of metrics for evaluating semantic similarity. We provide use cases to demonstrate how the proposed methods can be applied and computed, focusing on their interpretability and the universality of categorical constructions. This work contributes to the field by offering a novel perspective on semantic similarity and uncertainty metrics in language processing, generating criteria to automate their computation. Full article

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13 pages, 436 KiB

Open AccessArticle

Structural Stability of Pseudo-Parabolic Equations for Basic Data

by Yanping Wang and Yuanfei Li

Math. Comput. Appl. 2024, 29(6), 105; https://doi.org/10.3390/mca29060105 - 15 Nov 2024

This article investigates the spatial decay properties and continuous dependence on the basic geometric structure. Assuming that the total potential energy is bounded and the homogeneous Dirichlet condition is satisfied on the side of the solution within the cylindrical domain, we establish an [...] Read more.

This article investigates the spatial decay properties and continuous dependence on the basic geometric structure. Assuming that the total potential energy is bounded and the homogeneous Dirichlet condition is satisfied on the side of the solution within the cylindrical domain, we establish an auxiliary function related to the solution. By extending the data at the finite end forward, we can establish the continuous dependence on the perturbation of base data. Full article

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22 pages, 56577 KiB

Open AccessArticle

Resolving Contrast and Detail Trade-Offs in Image Processing with Multi-Objective Optimization

by Daniel Molina-Pérez and Alam Gabriel Rojas-López

Math. Comput. Appl. 2024, 29(6), 104; https://doi.org/10.3390/mca29060104 - 11 Nov 2024

This article addresses the complex challenge of simultaneously enhancing contrast and detail in an image, where improving one property often compromises the other. This trade-off is tackled using a multi-objective optimization approach. Specifically, the proposal’s model integrates the sigmoid transformation function and unsharp [...] Read more.

This article addresses the complex challenge of simultaneously enhancing contrast and detail in an image, where improving one property often compromises the other. This trade-off is tackled using a multi-objective optimization approach. Specifically, the proposal’s model integrates the sigmoid transformation function and unsharp masking highboost filtering with the NSGA-II algorithm. Additionally, a posterior preference articulation is introduced to select three key solutions from the Pareto front: the maximum contrast solution, the maximum detail solution, and the knee point solution. The proposed technique is evaluated on a range of image types, including medical and natural scenes. The final solutions demonstrated significant superiority in terms of contrast and detail compared to the original images. The three selected solutions, although all are optimal, captured distinct characteristics within the images, offering different solutions according to field preferences. This highlights the method’s effectiveness across different types and enhancement requirements and emphasizes the importance of the proposed preferences in different contexts. Full article

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

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16 pages, 504 KiB

Open AccessArticle

An Experimental Comparison of Self-Adaptive Differential Evolution Algorithms to Induce Oblique Decision Trees

by Rafael Rivera-López, Efrén Mezura-Montes, Juana Canul-Reich and Marco-Antonio Cruz-Chávez

Math. Comput. Appl. 2024, 29(6), 103; https://doi.org/10.3390/mca29060103 - 9 Nov 2024

This study addresses the challenge of generating accurate and compact oblique decision trees using self-adaptive differential evolution algorithms. Although traditional decision tree induction methods create explainable models, they often fail to achieve optimal classification accuracy. To overcome these limitations, other strategies, such as [...] Read more.

This study addresses the challenge of generating accurate and compact oblique decision trees using self-adaptive differential evolution algorithms. Although traditional decision tree induction methods create explainable models, they often fail to achieve optimal classification accuracy. To overcome these limitations, other strategies, such as those based on evolutionary computation, have been proposed in the literature. In particular, we evaluate the use of self-adaptive differential evolution variants to evolve a population of oblique decision trees encoded as real-valued vectors. Our proposal includes (1) an alternative initialization strategy that reduces redundant nodes and (2) a fitness function that penalizes excessive leaf nodes, promoting smaller and more accurate decision trees. We perform a comparative performance analysis of these differential evolution variants, showing that while they exhibit similar statistical behavior, the Single-Objective real-parameter optimization (jSO) method produces the most accurate oblique decision trees and is second best in compactness. The findings highlight the potential of self-adaptive differential evolution algorithms to improve the effectiveness of oblique decision trees in machine learning applications. Full article

(This article belongs to the Collection Feature Papers in Mathematical and Computational Applications 2024)

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Topic in Computation, MCA, Mathematics, Symmetry, Energies

Analytical and Numerical Models in Geo-Energy Topic Editors: Xiang Rao, Hao Xiong
Deadline: 31 December 2024

Topic in AppliedMath, Axioms, Fractal Fract, MCA, Mathematics, Symmetry

Fractional Calculus, Symmetry Phenomenon and Probability Theory for PDEs, and ODEs Topic Editors: Renhai Wang, Junesang Choi
Deadline: 30 April 2025

Topic in Axioms, Computation, Entropy, MCA, Mathematics, Symmetry

Numerical Methods for Partial Differential Equations Topic Editors: Pengzhan Huang, Yinnian He
Deadline: 30 June 2025

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15–16 October 2025 The 1st International Electronic Conference on Games (IECGA 2025)

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Special Issue in MCA

Radial Basis Functions Guest Editors: Benny Yiu-Chung Hon, Zhuojia Fu, Junpu Li
Deadline: 31 December 2024

Special Issue in MCA

New Trends in Biomathematics Guest Editors: Cristiana da Silva, Vera Afreixo
Deadline: 31 December 2024

Special Issue in MCA

Numerical and Evolutionary Optimization 2024 Guest Editors: Marcela Quiroz-Castellanos, Oliver Cuate, Leonardo Trujillo, Oliver Schütze
Deadline: 31 December 2024

Special Issue in MCA

New Trends in Computational Intelligence and Applications 2024 Guest Editors: Mario Graff, Héctor-Gabriel Acosta-Mesa
Deadline: 15 February 2025

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Topical Collections

Topical Collection in MCA

Mathematical Modelling of COVID-19 Collection Editor: Cristiana da Silva

Topical Collection in MCA

Numerical Optimization Reviews Collection Editor: Oliver Schütze

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