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Mathematics, Volume 12, Issue 12 (June-2 2024) – 147 articles

Cover Story (view full-size image): In this paper, we investigate a noncoercive nonlinear elliptic operator with a drift term in an unbounded domain. The singular first-order term grows as |E(x)||∇u|, where E(x) is a vector field in a suitable Morrey-type space. Our operator is derived from a stationary equation of diffusion–advection problems. We establish existence, regularity, and uniqueness theorems for a Dirichlet problem. To achieve our main results, we utilize the weak maximum principle and a priori estimates. View this paper
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18 pages, 6319 KiB  
Article
Back to Basics: The Power of the Multilayer Perceptron in Financial Time Series Forecasting
by Ana Lazcano, Miguel A. Jaramillo-Morán and Julio E. Sandubete
Mathematics 2024, 12(12), 1920; https://doi.org/10.3390/math12121920 - 20 Jun 2024
Viewed by 383
Abstract
The economic time series prediction literature has seen an increase in research leveraging artificial neural networks (ANNs), particularly the multilayer perceptron (MLP) and, more recently, transformer networks. These ANN models have shown superior accuracy compared to traditional techniques such as autoregressive integrated moving [...] Read more.
The economic time series prediction literature has seen an increase in research leveraging artificial neural networks (ANNs), particularly the multilayer perceptron (MLP) and, more recently, transformer networks. These ANN models have shown superior accuracy compared to traditional techniques such as autoregressive integrated moving average (ARIMA) models. The most recent models in the prediction of this type of neural network, such as recurrent or Transformers models, are composed of complex architectures that require sufficient processing capacity to address the problems, while MLP is based on densely connected layers and supervised learning. A deep understanding of the limitations is necessary to appropriately choose the ideal model for each of the prediction tasks. In this article, we show how a simple architecture such as the MLP allows a better adjustment than other models, including a shorter prediction time. This research is based on the premise that the use of the most recent models will not always allow better results. Full article
(This article belongs to the Special Issue Statistical Methods for Forecasting and Risk Analysis)
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18 pages, 318 KiB  
Article
Extended Efficient Multistep Solvers for Solving Equations in Banach Spaces
by Ramandeep Behl, Ioannis K. Argyros and Sattam Alharbi
Mathematics 2024, 12(12), 1919; https://doi.org/10.3390/math12121919 - 20 Jun 2024
Viewed by 353
Abstract
In this paper, we investigate the local and semilocal convergence of an iterative method for solving nonlinear systems of equations. We first establish the conditions under which these methods converge locally to the solution. Then, we extend our analysis to examine the semilocal [...] Read more.
In this paper, we investigate the local and semilocal convergence of an iterative method for solving nonlinear systems of equations. We first establish the conditions under which these methods converge locally to the solution. Then, we extend our analysis to examine the semilocal convergence of these methods, considering their behavior when starting from initial guesses that are not necessarily close to the solution. Iterative approaches for solving nonlinear systems of equations must take into account the radius of convergence, computable upper error bounds, and the uniqueness of solutions. These points have not been addressed in earlier studies. Moreover, we provide numerical examples to demonstrate the theoretical findings and compare the performance of these methods under different circumstances. Finally, we conclude that our examination offers a significant understanding of the convergence characteristics of previous iterative techniques for solving nonlinear equation systems. Full article
(This article belongs to the Section Computational and Applied Mathematics)
25 pages, 419 KiB  
Article
The Generalized Fox–Wright Function: The Laplace Transform, the Erdélyi–Kober Fractional Integral and Its Role in Fractional Calculus
by Jordanka Paneva-Konovska and Virginia Kiryakova
Mathematics 2024, 12(12), 1918; https://doi.org/10.3390/math12121918 - 20 Jun 2024
Viewed by 380
Abstract
In this paper, we consider and study in detail the generalized Fox–Wright function Ψ˜qp introduced in our recent work as an extension of the Fox–Wright function Ψqp. This special function can be seen as an important case [...] Read more.
In this paper, we consider and study in detail the generalized Fox–Wright function Ψ˜qp introduced in our recent work as an extension of the Fox–Wright function Ψqp. This special function can be seen as an important case of the so-called I-functions of Rathie and H¯-functions of Inayat-Hussain, that in turn extend the Fox H-functions and appear to include some Feynman integrals in statistical physics, in polylogarithms, in Riemann Zeta-type functions and in other important mathematical functions. Depending on the parameters, Ψ˜qp is an entire function or is analytic in an open disc with a final radius. We derive its basic properties, such as its order and type, and its images under the Laplace transform and under classical fractional-order integrals. Particular cases of Ψ˜qp are specified, including the Mittag-Leffler and Le Roy-type functions and their multi-index analogues and many other special functions of Fractional Calculus. The corresponding results are illustrated. Finally, we emphasize the role of these new generalized hypergeometric functions as eigenfunctions of operators of new Fractional Calculus with specific I-functions as singular kernels. This paper can be considered as a natural supplement to our previous surveys “Going Next after ‘A Guide to Special Functions in Fractional Calculus’: A Discussion Survey”, and “A Guide to Special Functions of Fractional Calculus”, published recently in this journal. Full article
(This article belongs to the Special Issue Fractional Calculus in Natural and Social Sciences)
24 pages, 1896 KiB  
Article
Energy–Logistics Cooperative Optimization for a Port-Integrated Energy System
by Aiming Mo, Yan Zhang, Yiyong Xiong, Fan Ma and Lin Sun
Mathematics 2024, 12(12), 1917; https://doi.org/10.3390/math12121917 - 20 Jun 2024
Viewed by 376
Abstract
In order to achieve carbon peak and neutrality goals, many low-carbon operations are implemented in ports. Integrated energy systems that consist of port electricity and cooling loads, wind and PV energy devices, energy storage, and clean fuels are considered as a future technology. [...] Read more.
In order to achieve carbon peak and neutrality goals, many low-carbon operations are implemented in ports. Integrated energy systems that consist of port electricity and cooling loads, wind and PV energy devices, energy storage, and clean fuels are considered as a future technology. In addition, ports are important hubs for the global economy and trade; logistics optimization is also part of their objective, and most port facilities have complex logistics. This article proposes an energy–logistics collaborative optimization method to fully tap the potential of port-integrated energy systems. A logistics–energy system model is established by deeply examining the operational characteristics of logistics systems and their corresponding energy consumption patterns, considering ships’ operational statuses, quay crane distribution constraints, and power balances. To better represent the ship–energy–logistics optimization problem, a hybrid system modeling technique is employed. The case of Shanghai Port is studied; the results show that costs can be reduced by 3.27% compared to the traditional optimization method, and a sensitivity analysis demonstrates the robustness of the proposed method. Full article
(This article belongs to the Special Issue Evolutionary Multi-Criteria Optimization: Methods and Applications)
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21 pages, 507 KiB  
Article
A Note on the Convergence of Multigrid Methods for the Riesz–Space Equation and an Application to Image Deblurring
by Danyal Ahmad, Marco Donatelli, Mariarosa Mazza, Stefano Serra-Capizzano and Ken Trotti
Mathematics 2024, 12(12), 1916; https://doi.org/10.3390/math12121916 - 20 Jun 2024
Viewed by 368
Abstract
In recent decades, a remarkable amount of research has been carried out regarding fast solvers for large linear systems resulting from various discretizations of fractional differential equations (FDEs). In the current work, we focus on multigrid methods for a Riesz–Space FDE whose theoretical [...] Read more.
In recent decades, a remarkable amount of research has been carried out regarding fast solvers for large linear systems resulting from various discretizations of fractional differential equations (FDEs). In the current work, we focus on multigrid methods for a Riesz–Space FDE whose theoretical convergence analysis of such multigrid methods is currently limited in the relevant literature to the two-grid method. Here we provide a detailed theoretical convergence study in the multilevel setting. Moreover, we discuss its use combined with a band approximation and we compare the result with both τ and circulant preconditionings. The numerical tests include 2D problems as well as the extension to the case of a Riesz–FDE with variable coefficients. Finally, we investigate the use of a Riesz–Space FDE in a variational model for image deblurring, comparing the performance of specific preconditioning strategies. Full article
(This article belongs to the Special Issue Mathematical Methods for Image Processing and Understanding)
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12 pages, 278 KiB  
Article
Bisection Series Approach for Exotic 3F2(1)-Series
by Marta Na Chen and Wenchang Chu
Mathematics 2024, 12(12), 1915; https://doi.org/10.3390/math12121915 - 20 Jun 2024
Viewed by 362
Abstract
By employing the bisection series approach, two classes of nonterminating 3F2(1)-series are examined. Several new summation formulae are established in closed form through the summation formulae of Gauss and Kummer for the 2 [...] Read more.
By employing the bisection series approach, two classes of nonterminating 3F2(1)-series are examined. Several new summation formulae are established in closed form through the summation formulae of Gauss and Kummer for the 2F1(±1)-series. They are expressed in terms of well-known functions such as π, Euler–Gamma, and logarithmic functions, which can be used in physics and applied sciences for numerical and theoretical analysis. Full article
(This article belongs to the Special Issue Integral Transforms and Special Functions in Applied Mathematics)
11 pages, 417 KiB  
Article
Sliding Mode Control of a Class of Hybrid-Switched Systems with Disturbances
by Jiaojiao Li, Yingying Wang and Jianyu Zhang
Mathematics 2024, 12(12), 1914; https://doi.org/10.3390/math12121914 - 20 Jun 2024
Viewed by 347
Abstract
This paper investigates the problem of sliding mode control for a class of hybrid switched systems with matching disturbances. Firstly, a sliding mode surface is designed, and the corresponding sliding mode equation for the switched system is derived. Then, we analyzed the stability [...] Read more.
This paper investigates the problem of sliding mode control for a class of hybrid switched systems with matching disturbances. Firstly, a sliding mode surface is designed, and the corresponding sliding mode equation for the switched system is derived. Then, we analyzed the stability of the sliding mode equation using the Lyapunov function and average dwell time. Moreover, a sliding mode control law is designed with the approach law method to drive the system state to a bounded sliding mode region and then maintain it there subsequently. Finally, an illustrative example is given to demonstrate the efficiency of the approach. Full article
(This article belongs to the Section Computational and Applied Mathematics)
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23 pages, 2359 KiB  
Article
Design and Implementation of Extremum-Seeking Control Based on MPPT for Dual-Axis Solar Tracker
by Cesar Ulises Solís-Cervantes, Sergio Isai Palomino-Resendiz, Diego Alonso Flores-Hernández, Marco Antonio Peñaloza-López and Carlos Manuel Montelongo-Vazquez
Mathematics 2024, 12(12), 1913; https://doi.org/10.3390/math12121913 - 20 Jun 2024
Viewed by 400
Abstract
The increase in the production efficiency of photovoltaic technology depends on its alignment in relation to the solar position. Solar tracking systems perform the tracking action by implementing control algorithms that help the reduction of tracking errors. However, conventional algorithms can reduce the [...] Read more.
The increase in the production efficiency of photovoltaic technology depends on its alignment in relation to the solar position. Solar tracking systems perform the tracking action by implementing control algorithms that help the reduction of tracking errors. However, conventional algorithms can reduce the life of actuators and mechanisms due to control action, significantly reducing operation times and profitability. In this article, an unconventional control scheme is developed to address the mentioned challenges, presenting the design and implementation of an extremum-seeking control to perform maximum power point tracking for a two-axis solar tracker instrumented with a solar module. The proposed controller is governed by the dynamics of a classic proportional-integral scheme and assisted by sensorless feedback. Also, it has an anti-wind-up-type configuration for the integral component and counts with a variable amplitude for the dither signal. The proposal is validated experimentally by comparison between a fixed system and a two-axis system in azimuth-elevation configuration. In addition, two performance indices are defined and analyzed, system energy production and tracking error. The results show that the proposal allows producing up to 27.75% more than a fixed system, considering the tracker energy consumption due to the tracking action and a pointing accuracy with ±1.8° deviation. Finally, an analysis and discussion are provided based on the results, concluding that the proposed algorithm is a viable alternative to increase the performance of tracked photovoltaic systems. Full article
(This article belongs to the Section Computational and Applied Mathematics)
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42 pages, 702 KiB  
Article
Stability Estimates of Optimal Solutions for the Steady Magnetohydrodynamics-Boussinesq Equations
by Gennadii Alekseev and Yuliya Spivak
Mathematics 2024, 12(12), 1912; https://doi.org/10.3390/math12121912 - 20 Jun 2024
Viewed by 399
Abstract
This paper develops the mathematical apparatus of studying control problems for the stationary model of magnetic hydrodynamics of viscous heat-conducting fluid in the Boussinesq approximation. These problems are formulated as problems of conditional minimization of special cost functionals by weak solutions of the [...] Read more.
This paper develops the mathematical apparatus of studying control problems for the stationary model of magnetic hydrodynamics of viscous heat-conducting fluid in the Boussinesq approximation. These problems are formulated as problems of conditional minimization of special cost functionals by weak solutions of the original boundary value problem. The model under consideration consists of the Navier–Stokes equations, the Maxwell equations without displacement currents, the generalized Ohm’s law for a moving medium and the convection-diffusion equation for temperature. These relations are nonlinearly connected via the Lorentz force, buoyancy force in the Boussinesq approximation and convective heat transfer. Results concerning the existence and uniqueness of the solution of the original boundary value problem and of its generalized linear analog are presented. The global solvability of the control problem under study is proved and the optimality system is derived. Sufficient conditions on the data are established which ensure local uniqueness and stability of solutions of the control problems under study with respect to small perturbations of the cost functional to be minimized and one of the given functions. We stress that the unique stability estimates obtained in the paper have a clear mathematical structure and intrinsic beauty. Full article
(This article belongs to the Special Issue Mathematical Problems in Fluid Mechanics)
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18 pages, 3517 KiB  
Article
Edge-Based Synchronization Control Criteria of Complex Dynamical Networks with Reaction–Diffusions
by Tao Xie, Qike Zhang and Xing Xiong
Mathematics 2024, 12(12), 1911; https://doi.org/10.3390/math12121911 - 20 Jun 2024
Viewed by 325
Abstract
This research investigates the edge-based asymptotic synchronization of delayed complex dynamical networks with reaction–diffusions and by an edge-based adaptive pinning control technique. Sufficient conditions for reaction–diffusion networks to realize synchronization are provided by Green’s formula, Wirtinger inequality, inequality analysis techniques, and contradiction methods. [...] Read more.
This research investigates the edge-based asymptotic synchronization of delayed complex dynamical networks with reaction–diffusions and by an edge-based adaptive pinning control technique. Sufficient conditions for reaction–diffusion networks to realize synchronization are provided by Green’s formula, Wirtinger inequality, inequality analysis techniques, and contradiction methods. The results show that network synchronization can be achieved by pinning any edge of the network (the choice of edge is arbitrary), which greatly reduces the difficulty of control. Lastly, a series of numerical examples illustrating the theoretical findings is provided. Full article
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22 pages, 7938 KiB  
Article
Short-Term Wind Speed Prediction for Bridge Site Area Based on Wavelet Denoising OOA-Transformer
by Yan Gao, Baifu Cao, Wenhao Yu, Lu Yi and Fengqi Guo
Mathematics 2024, 12(12), 1910; https://doi.org/10.3390/math12121910 - 20 Jun 2024
Viewed by 368
Abstract
Predicting wind speed in advance at bridge sites is essential for ensuring bridge construction safety under high wind conditions. This study proposes a short-term speed prediction model based on outlier correction, Wavelet Denoising, the Osprey Optimization Algorithm (OOA), and the Transformer model. The [...] Read more.
Predicting wind speed in advance at bridge sites is essential for ensuring bridge construction safety under high wind conditions. This study proposes a short-term speed prediction model based on outlier correction, Wavelet Denoising, the Osprey Optimization Algorithm (OOA), and the Transformer model. The outliers caused by data entry and measurement errors are processed by the interquartile range (IQR) method. By comparing the performance of four different wavelets, the best-performing wavelet (Bior2.2) was selected to filter out sharp noise from the data processed by the IQR method. The OOA-Transformer model was utilized to forecast short-term wind speeds based on the filtered time series data. With OOA-Transformer, the seven hyperparameters of the Transformer model were optimized by the Osprey Optimization Algorithm to achieve better performance. Given the outstanding performance of LSTM and its variants in wind speed prediction, the OOA-Transformer model was compared with six other models using the actual wind speed data from the Xuefeng Lake Bridge dataset to validate our proposed model. The experimental results show that the mean absolute percentage error (MAPE), root mean square error (RMSE), and coefficient of determination (R2) of this paper’s method on the test set were 4.16%, 0.0152, and 0.9955, respectively, which are superior to the other six models. The prediction accuracy was found to be high enough to meet the short-term wind speed prediction needs of practical projects. Full article
(This article belongs to the Special Issue Artificial Intelligence and Data Science)
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31 pages, 7137 KiB  
Article
Distributed Batch Learning of Growing Neural Gas for Quick and Efficient Clustering
by Chyan Zheng Siow, Azhar Aulia Saputra, Takenori Obo and Naoyuki Kubota
Mathematics 2024, 12(12), 1909; https://doi.org/10.3390/math12121909 - 20 Jun 2024
Viewed by 379
Abstract
Growing neural gas (GNG) has been widely used in topological mapping, clustering and unsupervised tasks. It starts from two random nodes and grows until it forms a topological network covering all data. The time required for growth depends on the total amount of [...] Read more.
Growing neural gas (GNG) has been widely used in topological mapping, clustering and unsupervised tasks. It starts from two random nodes and grows until it forms a topological network covering all data. The time required for growth depends on the total amount of data and the current network nodes. To accelerate growth, we introduce a novel distributed batch processing method to extract the rough distribution called Distributed Batch Learning Growing Neural Gas (DBL-GNG). First, instead of using a for loop in standard GNG, we adopt a batch learning approach to accelerate learning. To do this, we replace most of the standard equations with matrix calculations. Next, instead of starting with two random nodes, we start with multiple nodes in different distribution areas. Furthermore, we also propose to add multiple nodes to the network instead of adding them one by one. Finally, we introduce an edge cutting method to reduce unimportant links between nodes to obtain a better cluster network. We demonstrate DBL-GNG on multiple benchmark datasets. From the results, DBL-GNG performs faster than other GNG methods by at least 10 times. We also demonstrate the scalability of DBL-GNG by implementing a multi-scale batch learning process in it, named MS-DBL-GNG, which successfully obtains fast convergence results. In addition, we also demonstrate the dynamic data adaptation of DBL-GNG to 3D point cloud data. It is capable of processing and mapping topological nodes on point cloud objects in real time. Full article
(This article belongs to the Special Issue Advanced Machine Vision with Mathematics)
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15 pages, 267 KiB  
Article
New Upper Bounds for Covering Arrays of Order Seven
by Jose Torres-Jimenez and Idelfonso Izquierdo-Marquez
Mathematics 2024, 12(12), 1908; https://doi.org/10.3390/math12121908 - 20 Jun 2024
Viewed by 365
Abstract
A covering array is a combinatorial object that is used to test hardware and software components. The covering array number is the minimum number of rows needed to construct a specific covering array. The search for better upper bounds for covering array numbers [...] Read more.
A covering array is a combinatorial object that is used to test hardware and software components. The covering array number is the minimum number of rows needed to construct a specific covering array. The search for better upper bounds for covering array numbers is a very active area of research. Although there are many methods for defining new upper bounds for covering array numbers, recently the use of covering perfect hash families has significantly improved a large number of covering array numbers for alphabets that are prime powers. Currently, excellent upper bounds have been reported for alphabets 2, 3, 4, and 5; therefore, the focus of this article is on defining new upper bounds on the size of covering arrays for the alphabet seven using perfect hash families. For this purpose, a greedy column extension algorithm was constructed to increase the number of columns in a covering perfect hash family while keeping the number of rows constant. Our greedy algorithm begins with a random covering perfect hash family containing only eight columns and alternates between adding and removing columns. Adding columns increases the size of the covering perfect hash family while removing columns reduces the number of missing combinations in covering perfect hash families with different column counts. The construction process continues with the covering perfect hash family with the smallest number of columns being refined (i.e., missing combinations reduced). Thus, columns are dynamically added and removed to refine the covering perfect hash families being built. To illustrate the advantages of our greedy approach, 152 new covering perfect hash families of order seven with strengths 3, 4, 5, and 6 were constructed, enabling us to improve 12,556 upper bounds of covering array numbers; 903 of these improvements are for strength three, 8910 for strength four, 1957 for strength five, and 786 for strength six. Full article
1 pages, 119 KiB  
Correction
Correction: Li et al. Attitude Control of UAVs with Search Optimization and Disturbance Rejection Strategies. Mathematics 2023, 11, 3794
by Wensheng Li, Fanke Yang, Liqiang Zhong, Hao Wu, Xiangyuan Jiang and Andrei V. Chukalin
Mathematics 2024, 12(12), 1907; https://doi.org/10.3390/math12121907 - 20 Jun 2024
Viewed by 237
Abstract
In the original publication [...] Full article
0 pages, 14674 KiB  
Article
A Rumor Propagation Model Considering Media Effect and Suspicion Mechanism under Public Emergencies
by Shan Yang, Shihan Liu, Kaijun Su and Jianhong Chen
Mathematics 2024, 12(12), 1906; https://doi.org/10.3390/math12121906 - 19 Jun 2024
Viewed by 433
Abstract
In this paper, we collect the basic information data of online rumors and highly topical public opinions. In the research of the propagation model of online public opinion rumors, we use the improved SCIR model to analyze the characteristics of online rumor propagation [...] Read more.
In this paper, we collect the basic information data of online rumors and highly topical public opinions. In the research of the propagation model of online public opinion rumors, we use the improved SCIR model to analyze the characteristics of online rumor propagation under the suspicion mechanism at different propagation stages, based on considering the flow of rumor propagation. We analyze the stability of the evolution of rumor propagation by using the time-delay differential equation under the punishment mechanism. In this paper, the evolution of heterogeneous views with different acceptance and exchange thresholds is studied, using the standard Deffuant model and the improved model under the influence of the media, to analyze the evolution process and characteristics of rumor opinions. Based on the above results, it is found that improving the recovery rate is better than reducing the deception rate, and increasing the eviction rate is better than improving the detection rate. When the time lag τ < 110, it indicates that the spread of rumors tends to be asymptotic and stable, and the punishment mechanism can reduce the propagation time and the maximum proportion of deceived people. The proportion of deceived people increases with the decrease in the exchange threshold, and the range of opinion clusters increases with the decline in acceptance. Full article
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18 pages, 3259 KiB  
Article
Research on Vehicle AEB Control Strategy Based on Safety Time–Safety Distance Fusion Algorithm
by Xiang Fu, Jiaqi Wan, Daibing Wu, Wei Jiang, Wang Ma and Tianqi Yang
Mathematics 2024, 12(12), 1905; https://doi.org/10.3390/math12121905 - 19 Jun 2024
Viewed by 451
Abstract
With the increasing consumer focus on automotive safety, Autonomous Emergency Braking (AEB) systems, recognized as effective active safety technologies for collision avoidance and the mitigation of collision-related injuries, are gaining wider application in the automotive industry. To address the issues of the insufficient [...] Read more.
With the increasing consumer focus on automotive safety, Autonomous Emergency Braking (AEB) systems, recognized as effective active safety technologies for collision avoidance and the mitigation of collision-related injuries, are gaining wider application in the automotive industry. To address the issues of the insufficient working reliability of AEB systems and their unsatisfactory level of accordance with the psychological expectations of drivers, this study proposes an optimized second-order Time to Collision (TTC) safety time algorithm based on the motion state of the preceding vehicle. Additionally, the study introduces a safety distance algorithm derived from an analysis of the braking process of the main vehicle. The safety time algorithm focusing on comfort and the safety distance algorithm focusing on safety are effectively integrated in the time domain and the space domain to obtain the safety time–safety distance fusion algorithm. A MATLAB/Simulink–Carsim joint simulation platform has been established to validate the AEB control strategy in terms of safety, comfort, and system responsiveness. The simulation results show that the proposed safety time–safety distance fusion algorithm consistently achieves complete collision avoidance, indicating a higher safety level for the AEB system. Furthermore, the application of active hierarchical braking minimizes the distance error, at under 0.37 m, which meets psychological expectations of drivers and improves the comfort of the AEB system. Full article
(This article belongs to the Special Issue Modeling, Optimization and Control of Industrial Processes)
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28 pages, 4562 KiB  
Article
Exploring the Therapeutic Potential of Defective Interfering Particles in Reducing the Replication of SARS-CoV-2
by Macauley Locke, Dmitry Grebennikov, Igor Sazonov, Martín López-García, Marina Loguinova, Andreas Meyerhans, Gennady Bocharov and Carmen Molina-París
Mathematics 2024, 12(12), 1904; https://doi.org/10.3390/math12121904 - 19 Jun 2024
Viewed by 475
Abstract
SARS-CoV-2 still presents a global threat to human health due to the continued emergence of new strains and waning immunity among vaccinated populations. Therefore, it is still relevant to investigate potential therapeutics, such as therapeutic interfering particles (TIPs). Mathematical and computational modeling are [...] Read more.
SARS-CoV-2 still presents a global threat to human health due to the continued emergence of new strains and waning immunity among vaccinated populations. Therefore, it is still relevant to investigate potential therapeutics, such as therapeutic interfering particles (TIPs). Mathematical and computational modeling are valuable tools to study viral infection dynamics for predictive analysis. Here, we expand on the previous work on SARS-CoV-2 intra-cellular replication dynamics to include defective interfering particles (DIPs) as potential therapeutic agents. We formulate a deterministic model that describes the replication of wild-type (WT) SARS-CoV-2 virus in the presence of DIPs. Sensitivity analysis of parameters to several model outputs is employed to inform us on those parameters to be carefully calibrated from experimental data. We then study the effects of co-infection on WT replication and how DIP dose perturbs the release of WT viral particles. Furthermore, we provide a stochastic formulation of the model that is compared to the deterministic one. These models could be further developed into population-level models or used to guide the development and dose of TIPs. Full article
(This article belongs to the Special Issue Nonlinear Dynamics Research in Biomedicine)
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10 pages, 227 KiB  
Article
Bayesian Control Chart for Number of Defects in Production Quality Control
by Yadpirun Supharakonsakun
Mathematics 2024, 12(12), 1903; https://doi.org/10.3390/math12121903 - 19 Jun 2024
Viewed by 375
Abstract
This study investigates the extension of the c-chart control chart to Bayesian methodology, utilizing the gamma distribution to establish control limits. By comparing the performance of the Bayesian approach with that of two existing methods (the traditional frequentist method and the Bayesian with [...] Read more.
This study investigates the extension of the c-chart control chart to Bayesian methodology, utilizing the gamma distribution to establish control limits. By comparing the performance of the Bayesian approach with that of two existing methods (the traditional frequentist method and the Bayesian with Jeffreys method), we assess its effectiveness in terms of the average run lengths (ARLs) and false alarm rates (FARs). Simulation results indicate that the proposed Bayesian method consistently outperforms the existing techniques, offering larger ARLs and smaller FARs that closely approximate the expected nominal values. While the Bayesian approach excels in most scenarios, challenges may arise with large values of the λ parameter, necessitating adjustments to the hyperparameters of the gamma prior. Specifically, smaller values of the rate parameter are recommended for optimal performance. Overall, our findings suggest that the Bayesian extension of the c-chart provides a promising alternative for enhanced process monitoring and control. Full article
19 pages, 7458 KiB  
Article
A Method for Evaluating the Data Integrity of Microseismic Monitoring Systems in Mines Based on a Gradient Boosting Algorithm
by Cong Wang, Kai Zhan, Xigui Zheng, Cancan Liu and Chao Kong
Mathematics 2024, 12(12), 1902; https://doi.org/10.3390/math12121902 - 19 Jun 2024
Viewed by 407
Abstract
Microseismic data are widely employed for assessing rockburst risks; however, significant disparities exist in the monitoring capabilities of seismic networks across different mines, and none can capture a complete dataset of microseismic events. Such differences introduce unfairness when applying the same methodologies to [...] Read more.
Microseismic data are widely employed for assessing rockburst risks; however, significant disparities exist in the monitoring capabilities of seismic networks across different mines, and none can capture a complete dataset of microseismic events. Such differences introduce unfairness when applying the same methodologies to evaluate rockburst risks in various mines. This paper proposes a method for assessing the monitoring capability of seismic networks applicable to heterogeneous media in mines. It achieves this by integrating three gradient boosting algorithms: Extreme Gradient Boosting (XGBoost), Light Gradient Boosting Machine (LightGBM), and Categorical Boosting (CatBoost). Initially, the isolation forest algorithm is utilized for preliminary data cleansing, and feature engineering is constructed based on the relative locations of event occurrences to monitoring stations and the working face. Subsequently, the optimal hyperparameters for three models are searched for using 8508 microseismic events from the a Coal Mine in eastern China as samples, and 18 sub-models are trained. Model weights are then determined based on the performance metrics of different algorithms, and an ensemble model is created to predict the monitoring capability of the network. The model demonstrated excellent performance on the training and test sets, achieving log loss, accuracy, and recall scores of 7.13, 0.81, and 0.76 and 6.99, 0.80, and 0.77, respectively. Finally, the method proposed in this study was compared with traditional approaches. The results indicated that, under the same conditions, the proposed method calculated the monitoring capability of the key areas to be 11% lower than that of the traditional methods. The reasons for the differences between these methods were identified and partially explained. Full article
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16 pages, 15928 KiB  
Article
An Optimal ADMM for Unilateral Obstacle Problems
by Shougui Zhang, Xiyong Cui, Guihua Xiong and Ruisheng Ran
Mathematics 2024, 12(12), 1901; https://doi.org/10.3390/math12121901 - 19 Jun 2024
Viewed by 392
Abstract
We propose a new alternating direction method of multipliers (ADMM) with an optimal parameter for the unilateral obstacle problem. We first use the five-point difference scheme to discretize the problem. Then, we present an augmented Lagrangian by introducing an auxiliary unknown, and an [...] Read more.
We propose a new alternating direction method of multipliers (ADMM) with an optimal parameter for the unilateral obstacle problem. We first use the five-point difference scheme to discretize the problem. Then, we present an augmented Lagrangian by introducing an auxiliary unknown, and an ADMM is applied to the corresponding saddle-point problem. Through eliminating the primal and auxiliary unknowns, a pure dual algorithm is then used. The convergence of the proposed method is analyzed, and a simple strategy is presented for selecting the optimal parameter, with the largest and smallest eigenvalues of the iterative matrix. Several numerical experiments confirm the theoretical findings of this study. Full article
(This article belongs to the Special Issue Variational Inequality and Mathematical Analysis)
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24 pages, 3554 KiB  
Article
A Hybrid Reproducing Kernel Particle Method for Three-Dimensional Helmholtz Equation
by Piaopiao Peng, Ning Wang and Yumin Cheng
Mathematics 2024, 12(12), 1900; https://doi.org/10.3390/math12121900 - 19 Jun 2024
Viewed by 394
Abstract
The reproducing kernel particle method (RKPM) is one of the most universal meshless methods. However, when solving three-dimensional (3D) problems, the computational efficiency is relatively low because of the complexity of the shape function. To overcome this disadvantage, in this study, we introduced [...] Read more.
The reproducing kernel particle method (RKPM) is one of the most universal meshless methods. However, when solving three-dimensional (3D) problems, the computational efficiency is relatively low because of the complexity of the shape function. To overcome this disadvantage, in this study, we introduced the dimension splitting method into the RKPM to present a hybrid reproducing kernel particle method (HRKPM), and the 3D Helmholtz equation is solved. The 3D Helmholtz equation is transformed into a series of related two-dimensional (2D) ones, in which the 2D RKPM shape function is used, and the Galerkin weak form of these 2D problems is applied to obtain the discretized equations. In the dimension-splitting direction, the difference method is used to combine the discretized equations in all 2D domains. Three example problems are given to illustrate the performance of the HRKPM. Moreover, the numerical results show that the HRKPM can improve the computational efficiency of the RKPM significantly. Full article
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21 pages, 991 KiB  
Article
A Complex-Valued Stationary Kalman Filter for Positive and Negative Sequence Estimation in DER Systems
by Ricardo Pérez-Ibacache, Rodrigo Carvajal, Ramón Herrera-Hernández, Juan C. Agüero and César A. Silva
Mathematics 2024, 12(12), 1899; https://doi.org/10.3390/math12121899 - 19 Jun 2024
Viewed by 421
Abstract
In medium- and low-voltage three-phase distribution networks, the load imbalance among the phases may compromise the network voltage symmetry. Inverter-interfaced distributed energy resources (DERs) can contribute to compensating for such imbalances by sharing the required negative sequence current while providing active power synchronized [...] Read more.
In medium- and low-voltage three-phase distribution networks, the load imbalance among the phases may compromise the network voltage symmetry. Inverter-interfaced distributed energy resources (DERs) can contribute to compensating for such imbalances by sharing the required negative sequence current while providing active power synchronized with the positive sequence voltage. However, positive and negative sequences are conventionally defined in a steady state and are not directly observed from the instantaneous voltage and current measurements at the DER unit’s point of connection. In this article, an estimation algorithm for sequence separation based on the Kalman filter is proposed. Furthermore, the proposed filter uses a complex vector representation of the asymmetric three-phase signals in synchronous coordinates to allow for the implementation of the Kalman filter in its stationary form, resulting in a simple dynamic filter able to estimate positive and negative sequences even during transient operation. The proposed stationary complex Kalman filter performs better than state-of-the-art techniques like DSOGI and very similarly to other Kalman filter implementations found in the literature but at a fraction of its computational cost (23.5%). Full article
(This article belongs to the Section Engineering Mathematics)
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39 pages, 12684 KiB  
Article
Exploring Data Augmentation and Active Learning Benefits in Imbalanced Datasets
by Luis Moles, Alain Andres, Goretti Echegaray and Fernando Boto
Mathematics 2024, 12(12), 1898; https://doi.org/10.3390/math12121898 - 19 Jun 2024
Viewed by 399
Abstract
Despite the increasing availability of vast amounts of data, the challenge of acquiring labeled data persists. This issue is particularly serious in supervised learning scenarios, where labeled data are essential for model training. In addition, the rapid growth in data required by cutting-edge [...] Read more.
Despite the increasing availability of vast amounts of data, the challenge of acquiring labeled data persists. This issue is particularly serious in supervised learning scenarios, where labeled data are essential for model training. In addition, the rapid growth in data required by cutting-edge technologies such as deep learning makes the task of labeling large datasets impractical. Active learning methods offer a powerful solution by iteratively selecting the most informative unlabeled instances, thereby reducing the amount of labeled data required. However, active learning faces some limitations with imbalanced datasets, where majority class over-representation can bias sample selection. To address this, combining active learning with data augmentation techniques emerges as a promising strategy. Nonetheless, the best way to combine these techniques is not yet clear. Our research addresses this question by analyzing the effectiveness of combining both active learning and data augmentation techniques under different scenarios. Moreover, we focus on improving the generalization capabilities for minority classes, which tend to be overshadowed by the improvement seen in majority classes. For this purpose, we generate synthetic data using multiple data augmentation methods and evaluate the results considering two active learning strategies across three imbalanced datasets. Our study shows that data augmentation enhances prediction accuracy for minority classes, with approaches based on CTGANs obtaining improvements of nearly 50% in some cases. Moreover, we show that combining data augmentation techniques with active learning can reduce the amount of real data required. Full article
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18 pages, 318 KiB  
Article
Dynamics for a Ratio-Dependent Prey–Predator Model with Different Free Boundaries
by Lingyu Liu, Xiaobo Li and Pengcheng Li
Mathematics 2024, 12(12), 1897; https://doi.org/10.3390/math12121897 - 19 Jun 2024
Viewed by 291
Abstract
In this paper, we study the dynamics of the ratio-dependent type prey–predator model with different free boundaries. The two free boundaries, determined by prey and predator, respectively, implying that they may intersect with each other as time evolves, are used to describe the [...] Read more.
In this paper, we study the dynamics of the ratio-dependent type prey–predator model with different free boundaries. The two free boundaries, determined by prey and predator, respectively, implying that they may intersect with each other as time evolves, are used to describe the spreading of prey and predator. Our primary focus lies in analyzing the long-term behaviors of both predator and prey. We establish sufficient conditions for the spreading and vanishing of prey and predator. Furthermore, in cases where spread occurs, we offer estimates for the asymptotic spreading speeds of prey and predator, denoted as u and v, respectively, as well as the asymptotic speeds of the free boundaries, denoted by h and g. Our findings reveal that when the predator’s speed is lower than that of the prey, it leads to a reduction in the prey’s asymptotic speed. Full article
(This article belongs to the Special Issue Nonlinear Analysis and Application)
8 pages, 219 KiB  
Article
On Hyperbolic Equations with a Translation Operator in Lowest Derivatives
by Vladimir Vasilyev and Natalya Zaitseva
Mathematics 2024, 12(12), 1896; https://doi.org/10.3390/math12121896 - 19 Jun 2024
Viewed by 259
Abstract
In the half-plane, a solution to a two-dimensional hyperbolic equation with a translation operator in the lowest derivative with respect to a spatial variable varying along the entire real axis is constructed in an explicit form. It is proven that the solutions obtained [...] Read more.
In the half-plane, a solution to a two-dimensional hyperbolic equation with a translation operator in the lowest derivative with respect to a spatial variable varying along the entire real axis is constructed in an explicit form. It is proven that the solutions obtained are classical if the real part of the symbol of a differential-difference operator in the equation is positive. Full article
17 pages, 885 KiB  
Article
SSA-ELM: A Hybrid Learning Model for Short-Term Traffic Flow Forecasting
by Fei Wang, Yinxi Liang, Zhizhe Lin, Jinglin Zhou and Teng Zhou
Mathematics 2024, 12(12), 1895; https://doi.org/10.3390/math12121895 - 19 Jun 2024
Viewed by 433
Abstract
Nowadays, accurate and efficient short-term traffic flow forecasting plays a critical role in intelligent transportation systems (ITS). However, due to the fact that traffic flow is susceptible to factors such as weather and road conditions, traffic flow data tend to exhibit dynamic uncertainty [...] Read more.
Nowadays, accurate and efficient short-term traffic flow forecasting plays a critical role in intelligent transportation systems (ITS). However, due to the fact that traffic flow is susceptible to factors such as weather and road conditions, traffic flow data tend to exhibit dynamic uncertainty and nonlinearity, making the construction of a robust and reliable forecasting model still a challenging task. Aiming at this nonlinear and complex traffic flow forecasting problem, this paper constructs a short-term traffic flow forecasting hybrid optimization model, SSA-ELM, based on extreme learning machine by embedding the sparrow search algorithm in order to solve the above problem. Extreme learning machine has been widely used in short-term traffic flow forecasting due to its characteristics such as low computational complexity and fast learning speed. By using the sparrow search algorithm to optimize the input weight values and hidden layer deviations in the extreme learning machine, the sparrow search algorithm is utilized to search for the global optimal solution while taking into account the original characteristics of the extreme learning machine, so that the model improves stability while increasing prediction accuracy. Experimental results on the Amsterdam A10 road traffic flow dataset show that the traffic flow forecasting model proposed in this paper has higher forecasting accuracy and stability, revealing the potential of hybrid optimization models in the field of short-term traffic flow forecasting. Full article
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32 pages, 1978 KiB  
Article
A Multi-Criteria Assessment Model for Cooperative Technology Transfer Projects from Universities to Industries
by Rui Xiong, Hongyi Sun, Shufen Zheng and Sichu Liu
Mathematics 2024, 12(12), 1894; https://doi.org/10.3390/math12121894 - 18 Jun 2024
Viewed by 539
Abstract
Cooperative Technology Transfer (CTT) is a technology transfer model where universities and enterprises jointly participate throughout the entire process of technology transfer activities. Most discussions focus on its mechanisms and influencing factors, yet a framework to guide CTT projects in practice is still [...] Read more.
Cooperative Technology Transfer (CTT) is a technology transfer model where universities and enterprises jointly participate throughout the entire process of technology transfer activities. Most discussions focus on its mechanisms and influencing factors, yet a framework to guide CTT projects in practice is still lacking. This study proposes an assessment model based on the life-cycle of CTT projects, covering the initial cooperation relationship, project management during the mid-term, and technological achievements at the end. The model was evaluated by 14 experts first and then validated through two CTT projects in China. Gray Relation Analysis was employed to calculate the weights of different factors based on their relative importance, while the Dempster–Shafer theory was utilized to combine evidence from various sources and address the uncertainty in the assessment. The results of the case analysis indicate that the attitudes of universities and enterprises are considered critical in influencing the success of CTT projects, while management issues that arise during the projects can pose potential risks. This research serves as an applied exploration and has three functions. Firstly, the model can be used as a feasibility study before the project commences. Secondly, it can be utilized to analyze and improve potential issues during the project. Finally, it can be used for a post-project experience summary. Full article
(This article belongs to the Special Issue Multi-criteria Decision Making and Data Mining, 2nd Edition)
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25 pages, 6230 KiB  
Article
Fuzzy-Augmented Model Reference Adaptive PID Control Law Design for Robust Voltage Regulation in DC–DC Buck Converters
by Omer Saleem, Khalid Rasheed Ahmad and Jamshed Iqbal
Mathematics 2024, 12(12), 1893; https://doi.org/10.3390/math12121893 - 18 Jun 2024
Viewed by 450
Abstract
This paper presents a novel fuzzy-augmented model reference adaptive voltage regulation strategy for the DC–DC buck converters to enhance their resilience against random input variations and load-step transients. The ubiquitous proportional-integral-derivative (PID) controller is employed as the baseline scheme, whose gains are tuned [...] Read more.
This paper presents a novel fuzzy-augmented model reference adaptive voltage regulation strategy for the DC–DC buck converters to enhance their resilience against random input variations and load-step transients. The ubiquitous proportional-integral-derivative (PID) controller is employed as the baseline scheme, whose gains are tuned offline via a pre-calibrated linear-quadratic optimization scheme. However, owing to the inefficacy of the fixed-gain PID controller against parametric disturbances, it is retrofitted with a model reference adaptive controller that uses Lyapunov gain adaptation law for the online modification of PID gains. The adaptive controller is also augmented with an auxiliary fuzzy self-regulation system that acts as a superior regulator to dynamically update the adaptation rates of the Lyapunov gain adaptation law as a nonlinear function of the system’s classical error and its normalized acceleration. The proposed fuzzy system utilizes the knowledge of the system’s relative rate to execute better self-regulation of the adaptation rates, which in turn, flexibly steers the adaptability and response speed of the controller as the error conditions change. The propositions above are validated by performing tailored hardware experiments on a low-power DC–DC buck converter prototype. The experimental results validate the improved reference tracking and disturbance rejection ability of the proposed control law compared to the fixed PID controller. Full article
(This article belongs to the Special Issue Control, Optimization and Intelligent Computing in Energy)
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11 pages, 3912 KiB  
Article
Solution of the Elliptic Interface Problem by a Hybrid Mixed Finite Element Method
by Yuhan Wang, Peiyao Wang, Rongpei Zhang and Jia Liu
Mathematics 2024, 12(12), 1892; https://doi.org/10.3390/math12121892 - 18 Jun 2024
Viewed by 265
Abstract
This paper addresses the elliptic interface problem involving jump conditions across the interface. We propose a hybrid mixed finite element method on the triangulation where the interfaces are aligned with the mesh. The second-order elliptic equation is initially decomposed into two equations by [...] Read more.
This paper addresses the elliptic interface problem involving jump conditions across the interface. We propose a hybrid mixed finite element method on the triangulation where the interfaces are aligned with the mesh. The second-order elliptic equation is initially decomposed into two equations by introducing a gradient term. Subsequently, weak formulations are applied to these equations. Scheme continuity is enforced using the Lagrange multiplier technique. Finally, we derive an explicit formula for the entries of the matrix equation representing Lagrange multiplier unknowns resulting from hybridization. The method yields approximations of all variables, including the solution and gradient, with optimal order. Furthermore, the matrix representing the final linear algebra systems is not only symmetric but also positive definite. Numerical examples convincingly demonstrate the effectiveness of the hybrid mixed finite element method in addressing elliptic interface problems. Full article
(This article belongs to the Section Mathematics and Computer Science)
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17 pages, 4881 KiB  
Article
Dynamic Analysis and FPGA Implementation of a New Linear Memristor-Based Hyperchaotic System with Strong Complexity
by Lijuan Chen, Mingchu Yu, Jinnan Luo, Jinpeng Mi, Kaibo Shi and Song Tang
Mathematics 2024, 12(12), 1891; https://doi.org/10.3390/math12121891 - 18 Jun 2024
Viewed by 334
Abstract
Chaotic or hyperchaotic systems have a significant role in engineering applications such as cryptography and secure communication, serving as primary signal generators. To ensure stronger complexity, memristors with sufficient nonlinearity are commonly incorporated into the system, suffering a limitation on the physical implementation. [...] Read more.
Chaotic or hyperchaotic systems have a significant role in engineering applications such as cryptography and secure communication, serving as primary signal generators. To ensure stronger complexity, memristors with sufficient nonlinearity are commonly incorporated into the system, suffering a limitation on the physical implementation. In this paper, we propose a new four-dimensional (4D) hyperchaotic system based on the linear memristor which is the most straightforward to implement physically. Through numerical studies, we initially demonstrate that the proposed system exhibits robust hyperchaotic behaviors under typical parameter conditions. Subsequently, we theoretically prove the existence of solid hyperchaos by combining the topological horseshoe theory with computer-assisted research. Finally, we present the realization of the proposed hyperchaotic system using an FPGA platform. This proposed system possesses two key properties. Firstly, this work suggests that the simplest memristor can also induce strong nonlinear behaviors, offering a new perspective for constructing memristive systems. Secondly, compared to existing systems, our system not only has the largest Kaplan-Yorke dimension, but also has clear advantages in areas related to engineering applications, such as the parameter range and signal bandwidth, indicating promising potential in engineering applications. Full article
(This article belongs to the Special Issue Advance in Control Theory and Optimization)
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