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Mathematics
Volume 13
Issue 15
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Mathematics, Volume 13, Issue 15 (August-1 2025) – 217 articles

Cover Story (view full-size image): High-order reconstruction of piecewise-smooth functions is hampered by Gibbs oscillations near sharp transitions. The figure illustrates our Robust Discontinuity Indicator (RDI), which directly addresses this issue. The upper-left shows the input: function values on a spherical mesh. RDI processes the data in a single pass, combining a theoretically grounded cell-based overshoot indicator with a node-based oscillation indicator. The lower-right shows the output: a clean map that pinpoints C0 (value) and C1 (gradient) discontinuities. RDI handles complex geometry and nonuniform, unstructured meshes while producing fewer false positives than two-pass methods, enabling more reliable remapping and high-order simulations. View this paper
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17 pages, 2359 KiB  
Article
Safety Analysis of Subway Station Under Seepage Force Using a Continuous Velocity Field
by Zhufeng Cheng, De Zhou, Qiang Chen and Shuaifu Gu
Mathematics 2025, 13(15), 2541; https://doi.org/10.3390/math13152541 - 7 Aug 2025
Viewed by 133
Abstract
Groundwater is an important factor for the stability of the subway station pit constructed in the offshore area. To reflect the effects of groundwater drawdown on the stability of the station pit, this work uses a surface settlement formula based on Rayleigh distribution [...] Read more.
Groundwater is an important factor for the stability of the subway station pit constructed in the offshore area. To reflect the effects of groundwater drawdown on the stability of the station pit, this work uses a surface settlement formula based on Rayleigh distribution to construct a continuous deformation velocity field based on Terzaghi’s mechanism, so as to derive a theoretical calculation method for the safety factor of the deep station pit anti-uplift considering the effect of seepage force. Taking the seepage force as an external load acting on the soil skeleton, a simplified calculation method is proposed to describe the variation in shear strength with depth. Substituting the external work rate induced by self-weight, surface surcharge, seepage force, and plastic shear energy into the energy equilibrium equation, an explicit expression of the safety factor of the station pit is obtained. According to the parameter study and engineering application analysis, the validity and applicability of the proposed procedure are discussed. The parameter study indicated that deep excavation pits are significantly affected by construction drawdown and seepage force; the presence of seepage, to some extent, reduces the anti-uplift stability of the station pit. The calculation method in this work helps to compensate for the shortcomings of existing methods and has a higher accuracy in predicting the safety and stability of station pits under seepage situations. Full article
(This article belongs to the Special Issue Multiscale Modeling in Engineering and Mechanics: From Microscopic to Macroscopic Mechanical Modeling)
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55 pages, 3080 KiB  
Review
Controlling Sedimentation in Magnetorheological Fluids Through Ultrasound–Magnetic Field Coupling: Multiscale Analysis and Applications
by Annunziata Palumbo and Mario Versaci
Mathematics 2025, 13(15), 2540; https://doi.org/10.3390/math13152540 - 7 Aug 2025
Viewed by 147
Abstract
Magnetorheological fluids (MRFs) are multiphase materials whose viscosity can be controlled via magnetic fields. However, particle sedimentation undermines their long-term stability. This review examines stabilization strategies based on the interaction between ultrasonic waves and time-varying magnetic fields, analyzed through advanced mathematical models. The [...] Read more.
Magnetorheological fluids (MRFs) are multiphase materials whose viscosity can be controlled via magnetic fields. However, particle sedimentation undermines their long-term stability. This review examines stabilization strategies based on the interaction between ultrasonic waves and time-varying magnetic fields, analyzed through advanced mathematical models. The propagation of acoustic waves in spherical and cylindrical domains is studied, including effects such as cavitation, acoustic radiation forces, and viscous attenuation. The Biot–Stoll poroelastic model is employed to describe saturated granular media, while magnetic field modulation is investigated as a means to balance gravitational settling. The analysis highlights how acousto-magnetic coupling supports the design of programmable and self-stabilizing intelligent fluids for complex applications. Full article
(This article belongs to the Special Issue Engineering Thermodynamics and Fluid Mechanics)
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31 pages, 3735 KiB  
Article
An Analysis of Layer-Freezing Strategies for Enhanced Transfer Learning in YOLO Architectures
by Andrzej D. Dobrzycki, Ana M. Bernardos and José R. Casar
Mathematics 2025, 13(15), 2539; https://doi.org/10.3390/math13152539 - 7 Aug 2025
Viewed by 239
Abstract
The You Only Look Once (YOLO) architecture is crucial for real-time object detection. However, deploying it in resource-constrained environments such as unmanned aerial vehicles (UAVs) requires efficient transfer learning. Although layer freezing is a common technique, the specific impact of various freezing configurations [...] Read more.
The You Only Look Once (YOLO) architecture is crucial for real-time object detection. However, deploying it in resource-constrained environments such as unmanned aerial vehicles (UAVs) requires efficient transfer learning. Although layer freezing is a common technique, the specific impact of various freezing configurations on contemporary YOLOv8 and YOLOv10 architectures remains unexplored, particularly with regard to the interplay between freezing depth, dataset characteristics, and training dynamics. This research addresses this gap by presenting a detailed analysis of layer-freezing strategies. We systematically investigate multiple freezing configurations across YOLOv8 and YOLOv10 variants using four challenging datasets that represent critical infrastructure monitoring. Our methodology integrates a gradient behavior analysis (L2 norm) and visual explanations (Grad-CAM) to provide deeper insights into training dynamics under different freezing strategies. Our results reveal that there is no universal optimal freezing strategy but, rather, one that depends on the properties of the data. For example, freezing the backbone is effective for preserving general-purpose features, while a shallower freeze is better suited to handling extreme class imbalance. These configurations reduce graphics processing unit (GPU) memory consumption by up to 28% compared to full fine-tuning and, in some cases, achieve mean average precision (mAP@50) scores that surpass those of full fine-tuning. Gradient analysis corroborates these findings, showing distinct convergence patterns for moderately frozen models. Ultimately, this work provides empirical findings and practical guidelines for selecting freezing strategies. It offers a practical, evidence-based approach to balanced transfer learning for object detection in scenarios with limited resources. Full article
(This article belongs to the Special Issue Artificial Intelligence: Deep Learning and Computer Vision)
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15 pages, 326 KiB  
Article
The Set of Numerical Semigroups with Frobenius Number Belonging to a Fixed Interval
by María Ángeles Moreno-Frías and José Carlos Rosales
Mathematics 2025, 13(15), 2538; https://doi.org/10.3390/math13152538 - 7 Aug 2025
Viewed by 179
Abstract
Let a and b be positive integers such that a<b and [a,b]={x∈N∣a≤x≤b}. In this work, we will show that [...] Read more.
Let a and b be positive integers such that a<b and [a,b]={x∈N∣a≤x≤b}. In this work, we will show that A([a,b])={S∣S is a numerical semigroup whose Frobenius number belongs to [a,b]} and is a covariety. This fact allows us to present an algorithm which computes all the elements from A([a,b]). We will prove that A([a,b],m)={S∈A([a,b])∣S has multiplicity m} and is a ratio-covariety. As a consequence, we will show an algorithm which calculates all the elements belonging to A([a,b],m). Based on the above results, we will develop an interesting algorithm that calculates all numerical semigroups with a given multiplicity and complexity. Full article
18 pages, 1152 KiB  
Article
Coordinated Truck Loading and Routing Problem: A Forestry Logistics Case Study
by Cristian Oliva, Manuel Cepeda and Sebastián Muñoz-Herrera
Mathematics 2025, 13(15), 2537; https://doi.org/10.3390/math13152537 - 7 Aug 2025
Viewed by 196
Abstract
This study addresses a real-world logistics problem in forestry operations: the distribution of plants from cultivation centers to planting sites under strict delivery time windows and limited depot resources. We introduce the Coordinated Truck Loading and Routing Problem (CTLRP), an extension of the [...] Read more.
This study addresses a real-world logistics problem in forestry operations: the distribution of plants from cultivation centers to planting sites under strict delivery time windows and limited depot resources. We introduce the Coordinated Truck Loading and Routing Problem (CTLRP), an extension of the classical Vehicle Routing Problem with Time Windows (VRPTW) that integrates routing decisions with truck loading schedules at a single depot with constrained capacity. To solve this NP-hard problem, we develop a metaheuristic algorithm based on Ant Colony Optimization (ACO), enhanced with a global memory system and a novel stochastic return rule that allows trucks to return to the depot when additional deliveries are suboptimal. Parameter calibration experiments are conducted to determine optimal values for the return probability and ant population size. The algorithm is tested on a real forestry dispatch scenario over six working days. The results show that an Ant Colony System (ACS–CTLRP) algorithm reduces total distance traveled by 23%, travel time by 22%, and the number of trucks used by 13 units, while increasing fleet utilization from 54% to 83%. These findings demonstrate that the proposed method significantly outperforms current company planning and offers a transferable framework for depot-constrained routing problems in time-sensitive distribution environments. Full article
(This article belongs to the Special Issue New Advances and Applications Operational Research and Scheduling Theory)
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30 pages, 2584 KiB  
Article
Travel Frequent-Route Identification Based on the Snake Algorithm Using License Plate Recognition Data
by Feiyang Liu, Jie Zeng, Jinjun Tang and TianJian Yu
Mathematics 2025, 13(15), 2536; https://doi.org/10.3390/math13152536 - 7 Aug 2025
Viewed by 134
Abstract
Path flow always plays a critical role in extracting vehicle travel patterns and reflecting network-scale traffic features. However, the comprehensive topological structure of urban road networks induces massive route choices, so frequent travel routes have been gradually regarded as an ideal countermeasure to [...] Read more.
Path flow always plays a critical role in extracting vehicle travel patterns and reflecting network-scale traffic features. However, the comprehensive topological structure of urban road networks induces massive route choices, so frequent travel routes have been gradually regarded as an ideal countermeasure to represent traffic states. Widely used license plate recognition (LPR) devices can collect the abundant traffic features of all vehicles, but their sparse spatial distributions restrict the conventional models in frequent travel identification. Therefore, this study develops a network reconstruction method to construct a topological network from the LPR dataset, avoiding the adverse effects caused by the sparse distribution of detectors on the road network and further uses the Snake algorithm to fully utilize the road network structure and traffic attributes for clustering to obtain various travel patterns, with frequent routes under different travel patterns finally identified based on Steiner trees and frequent item recognition. To address the sparse spatial distribution of LPR devices, we utilize the word2vec model to extract spatial correlations among intersections. A threshold-based method is then applied to transform the correlation matrix into a reconstructed network, connecting intersections with strong vehicle transition relationships. This community structure can be interpreted as representing different travel patterns. Consequently, the Snake algorithm is employed to cluster intersections into distinct categories, reflecting these varied travel patterns. By leveraging the word2vec model, the detector installation rate requirement for Snake is significantly reduced, ensuring that the clustering results accurately represent the intrinsic relevance of traffic roads. Subsequently, frequent routes are identified from both macro- and micro-perspectives using the Steiner tree and Frequent Pattern Growth (FP Growth) algorithm, respectively. Validated on the LPR dataset in Changsha, China, the experiment results demonstrate that the proposed method can effectively identify travel patterns and extract frequent routes in the sparsely installed LPR devices. Full article
(This article belongs to the Special Issue Application of Mathematical Methods to Transportation: Modeling and Analysis)
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16 pages, 53970 KiB  
Article
UNet–Transformer Hybrid Architecture for Enhanced Underwater Image Processing and Restoration
by Jie Ji and Jiaju Man
Mathematics 2025, 13(15), 2535; https://doi.org/10.3390/math13152535 - 6 Aug 2025
Viewed by 209
Abstract
Underwater image enhancement is crucial for fields like marine exploration, underwater photography, and environmental monitoring, as underwater images often suffer from reduced visibility, color distortion, and contrast loss due to light absorption and scattering. Despite recent progress, existing methods struggle to generalize across [...] Read more.
Underwater image enhancement is crucial for fields like marine exploration, underwater photography, and environmental monitoring, as underwater images often suffer from reduced visibility, color distortion, and contrast loss due to light absorption and scattering. Despite recent progress, existing methods struggle to generalize across diverse underwater conditions, such as varying turbidity levels and lighting. This paper proposes a novel hybrid UNet–Transformer architecture based on MaxViT blocks, which effectively combines local feature extraction with global contextual modeling to address challenges including low contrast, color distortion, and detail degradation. Extensive experiments on two benchmark datasets, UIEB and EUVP, demonstrate the superior performance of our method. On UIEB, our model achieves a PSNR of 22.91, SSIM of 0.9020, and CCF of 37.93—surpassing prior methods such as URSCT-SESR and PhISH-Net. On EUVP, it attains a PSNR of 26.12 and PCQI of 1.1203, outperforming several state-of-the-art baselines in both visual fidelity and perceptual quality. These results validate the effectiveness and robustness of our approach under complex underwater degradation, offering a reliable solution for real-world underwater image enhancement tasks. Full article
(This article belongs to the Special Issue Algorithms, Models and Proofs: Advancing Scalability, Sustainability and Security in Large-Scale Computation and Cryptography)
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21 pages, 351 KiB  
Article
Using Pseudo-Complemented Truth Values of Calculation Errors in Integral Transforms and Differential Equations Through Monte Carlo Algorithms
by Ravi A. Salim, Ernastuti, Edi Sukirman, Trini Saptariani and Suryadi MT
Mathematics 2025, 13(15), 2534; https://doi.org/10.3390/math13152534 - 6 Aug 2025
Viewed by 187
Abstract
This study aims to demonstrate how mathematics, especially calculus concepts, can be expanded to include semi-entities and how these can be applied to sampling activities. Here, the multivalued logic uses pseudo-complemented lattices, instead of Boolean algebras. Truth values can express the intensity of [...] Read more.
This study aims to demonstrate how mathematics, especially calculus concepts, can be expanded to include semi-entities and how these can be applied to sampling activities. Here, the multivalued logic uses pseudo-complemented lattices, instead of Boolean algebras. Truth values can express the intensity of a property: for example, the property of being heavy intensifies as weight increases. They can also express the state-of-the-art knowledge of an individual about a certain thing. To express that a number x approaches a is to say that the statement “x=b” is not fully true but approaches the full-true value as b−a approaches zero. This approach generalizes the concept of a limit and the concepts derived from it, such as differentiation and integration. A Monte Carlo algorithm replaces one function with another with finite domain, preferably its finite part, by sampling the domain and calculating its map. The discussion extends to integration over an unbounded interval, integral transforms, and differential equations. This study then covers strategies for producing Monte Carlo estimates of respective problems and determining their crucial truth values. In the discussion, a topic related to axiomatizing set theory is also suggested. Full article
19 pages, 1090 KiB  
Article
Inbound Truck Scheduling for Workload Balancing in Cross-Docking Terminals
by Younghoo Noh, Seokchan Lee, Jeongyoon Hong, Jeongeum Kim and Sung Won Cho
Mathematics 2025, 13(15), 2533; https://doi.org/10.3390/math13152533 - 6 Aug 2025
Viewed by 221
Abstract
The rapid growth of e-commerce and advances in information and communication technologies have placed increasing pressure on last-mile delivery companies to enhance operational productivity. As investments in logistics infrastructure require long-term planning, maximizing the efficiency of existing terminal operations has become a critical [...] Read more.
The rapid growth of e-commerce and advances in information and communication technologies have placed increasing pressure on last-mile delivery companies to enhance operational productivity. As investments in logistics infrastructure require long-term planning, maximizing the efficiency of existing terminal operations has become a critical priority. This study proposes a mathematical model for inbound truck scheduling that simultaneously minimizes truck waiting times and balances workload across temporary inventory storage located at outbound chutes in cross-docking terminals. The model incorporates a dynamic rescheduling strategy that updates the assignment of inbound trucks in real time, based on the latest terminal conditions. Numerical experiments, based on real operational data, demonstrate that the proposed approach significantly outperforms conventional strategies such as First-In First-Out (FIFO) and Random assignment in terms of both load balancing and truck turnaround efficiency. In particular, the proposed model improves workload balance by approximately 10% and 12% compared to the FIFO and Random strategies, respectively, and it reduces average truck waiting time by 17% and 18%, thereby contributing to more efficient workflow and alleviating bottlenecks. The findings highlight the practical potential of the proposed strategy for improving the responsiveness and efficiency of parcel distribution centers operating under fixed infrastructure constraints. Future research may extend the proposed approach by incorporating realistic operational factors, such as cargo heterogeneity, uncertain arrivals, and terminal shutdowns due to limited chute storage. Full article
(This article belongs to the Special Issue Advances in Mathematical Modeling and Optimization for Business Analytics)
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13 pages, 281 KiB  
Article
Some Calibration Estimators of the Mean of a Sensitive Variable Under Measurement Error
by Sat Gupta, Pidugu Trisandhya and Frank Coolen
Mathematics 2025, 13(15), 2532; https://doi.org/10.3390/math13152532 - 6 Aug 2025
Viewed by 181
Abstract
This study explores the estimation of the mean of a sensitive variable using calibration estimators under measurement error. Three randomized response techniques are evaluated: Partial Randomized Response Technique, Compulsory Randomized Response Technique, and Optional Randomized Response Technique. Theoretical properties of the proposed estimators [...] Read more.
This study explores the estimation of the mean of a sensitive variable using calibration estimators under measurement error. Three randomized response techniques are evaluated: Partial Randomized Response Technique, Compulsory Randomized Response Technique, and Optional Randomized Response Technique. Theoretical properties of the proposed estimators are analyzed, and a simulation study using real COVID-19 infection data is conducted. Results indicate that the Optional Randomized Response Technique outperforms Partial Randomized Response Technique and Compulsory Randomized Response Technique in terms of efficiency, underscoring its effectiveness and practical utility for improving data quality in sensitive survey settings. Full article
11 pages, 2717 KiB  
Article
Finite Element Dynamic Modeling of Smart Structures and Adaptive Backstepping Control
by Zhipeng Xie, Dachang Zhu, Zhenzhang Liu, Yun Long and Fangyi Li
Mathematics 2025, 13(15), 2531; https://doi.org/10.3390/math13152531 - 6 Aug 2025
Viewed by 175
Abstract
Smart structures with topological configurations that integrate perception and actuation have complex geometric features. The simplification of these features can lead to deviations in dynamic characteristics, making it difficult to establish an accurate dynamic model. Uncertainties, such as material nonlinearity, hysteresis in elastic [...] Read more.
Smart structures with topological configurations that integrate perception and actuation have complex geometric features. The simplification of these features can lead to deviations in dynamic characteristics, making it difficult to establish an accurate dynamic model. Uncertainties, such as material nonlinearity, hysteresis in elastic deformation, and external disturbances, affect the trajectory tracking accuracy of the smart structure’s actuation function. This paper proposes a modeling method that combines finite element unit bodies and orthogonal characteristic mode reduction to construct an accurate dynamic model of the smart structure and design an adaptive backstepping controller. Nonlinear dynamic equations are derived through a finite element analysis of the structure, and the orthogonal characteristic mode reduction method is employed to reduce computational complexity while ensuring model accuracy. An adaptive backstepping controller is designed to mitigate model uncertainties and achieve precise trajectory tracking control. Simulation and experimental results demonstrate that the proposed method can effectively handle the nonlinearity and modeling errors of smart structures, achieving high-precision trajectory tracking and verifying the accuracy of the dynamic model as well as the robustness of the controller. Full article
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34 pages, 3002 KiB  
Article
A Refined Fuzzy MARCOS Approach with Quasi-D-Overlap Functions for Intuitive, Consistent, and Flexible Sensor Selection in IoT-Based Healthcare Systems
by Mahmut Baydaş, Safiye Turgay, Mert Kadem Ömeroğlu, Abdulkadir Aydin, Gıyasettin Baydaş, Željko Stević, Enes Emre Başar, Murat İnci and Mehmet Selçuk
Mathematics 2025, 13(15), 2530; https://doi.org/10.3390/math13152530 - 6 Aug 2025
Viewed by 312
Abstract
Sensor selection in IoT-based smart healthcare systems is a complex fuzzy decision-making problem due to the presence of numerous uncertain and interdependent evaluation criteria. Traditional fuzzy multi-criteria decision-making (MCDM) approaches often assume independence among criteria and rely on aggregation operators that impose sharp [...] Read more.
Sensor selection in IoT-based smart healthcare systems is a complex fuzzy decision-making problem due to the presence of numerous uncertain and interdependent evaluation criteria. Traditional fuzzy multi-criteria decision-making (MCDM) approaches often assume independence among criteria and rely on aggregation operators that impose sharp transitions between preference levels. These assumptions can lead to decision outcomes with insufficient differentiation, limited discriminatory capacity, and potential issues in consistency and sensitivity. To overcome these limitations, this study proposes a novel fuzzy decision-making framework by integrating Quasi-D-Overlap functions into the fuzzy MARCOS (Measurement of Alternatives and Ranking According to Compromise Solution) method. Quasi-D-Overlap functions represent a generalized extension of classical overlap operators, capable of capturing partial overlaps and interdependencies among criteria while preserving essential mathematical properties such as associativity and boundedness. This integration enables a more intuitive, flexible, and semantically rich modeling of real-world fuzzy decision problems. In the context of real-time health monitoring, a case study is conducted using a hybrid edge–cloud architecture, involving sensor tasks such as heartrate monitoring and glucose level estimation. The results demonstrate that the proposed method provides greater stability, enhanced discrimination, and improved responsiveness to weight variations compared to traditional fuzzy MCDM techniques. Furthermore, it effectively supports decision-makers in identifying optimal sensor alternatives by balancing critical factors such as accuracy, energy consumption, latency, and error tolerance. Overall, the study fills a significant methodological gap in fuzzy MCDM literature and introduces a robust fuzzy aggregation strategy that facilitates interpretable, consistent, and reliable decision making in dynamic and uncertain healthcare environments. Full article
(This article belongs to the Special Issue Advances in Multiple-Criteria Decision Making: New Trends and Applications)
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14 pages, 302 KiB  
Article
On Surfaces of Exceptional Lorentzian Lie Groups with a Four-Dimensional Isometry Group
by Giovanni Calvaruso and Lorenzo Pellegrino
Mathematics 2025, 13(15), 2529; https://doi.org/10.3390/math13152529 - 6 Aug 2025
Viewed by 193
Abstract
In total, geodesic surfaces and their generalizations, namely totally umbilical and parallel surfaces, are well-known topics in Submanifold Theory and have been intensively studied in three-dimensional ambient spaces, both Riemannian and Lorentzian. In this paper, we prove the non-existence of parallel and totally [...] Read more.
In total, geodesic surfaces and their generalizations, namely totally umbilical and parallel surfaces, are well-known topics in Submanifold Theory and have been intensively studied in three-dimensional ambient spaces, both Riemannian and Lorentzian. In this paper, we prove the non-existence of parallel and totally umbilical (in particular, totally geodesic) surfaces for three-dimensional Lorentzian Lie groups, which admit a four-dimensional isometry group, but are neither of Bianchi–Cartan–Vranceanu-type nor homogeneous plane waves. Consequently, the results of the present paper complete the investigation of these fundamental types of surfaces in all homogeneous Lorentzian manifolds, whose isometry group is four-dimensional. As a byproduct, we describe a large class of flat surfaces of constant mean curvature in these ambient spaces and exhibit a family of examples. Full article
(This article belongs to the Special Issue Recent Studies in Differential Geometry and Its Applications)
24 pages, 1690 KiB  
Article
Neural Network-Based Predictive Control of COVID-19 Transmission Dynamics to Support Institutional Decision-Making
by Cristina-Maria Stăncioi, Iulia Adina Ștefan, Violeta Briciu, Vlad Mureșan, Iulia Clitan, Mihail Abrudean, Mihaela-Ligia Ungureșan, Radu Miron, Ecaterina Stativă, Michaela Nanu, Adriana Topan and Ioana Nanu
Mathematics 2025, 13(15), 2528; https://doi.org/10.3390/math13152528 - 6 Aug 2025
Viewed by 178
Abstract
The COVID-19 pandemic was a profoundly influential global occurrence in recent history, impacting daily life, economics, and healthcare systems for an extended period. The abundance of data has been essential in creating models to simulate and forecast the dissemination of infectious illnesses, aiding [...] Read more.
The COVID-19 pandemic was a profoundly influential global occurrence in recent history, impacting daily life, economics, and healthcare systems for an extended period. The abundance of data has been essential in creating models to simulate and forecast the dissemination of infectious illnesses, aiding governments and health organizations in making educated decisions. This research primarily focuses on designing a control technique that incorporates the five most important inputs that impact the spread of COVID-19 on the Romanian territory. Quantitative analysis and data filtering are two crucial aspects to consider when developing a mathematical model. In this study the transfer function principle was used as the most accurate method for modeling the system, based on its superior fit demonstrated in a previous study. For the control strategy, a PI (Proportional-Integral) controller was designed to meet the requirements of the intended behavior. Finally, it is showed that for such complex models, the chosen control strategy, combined with fine tuning, led to very accurate results. Full article
(This article belongs to the Special Issue Control Theory and Applications, 2nd Edition)
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42 pages, 13005 KiB  
Article
A Numerical Investigation of Plastic Energy Dissipation Patterns of Circular and Non-Circular Metal Thin-Walled Rings Under Quasi-Static Lateral Crushing
by Shunsong Guo, Sunting Yan, Ping Tang, Chenfeng Guan and Wei Zhang
Mathematics 2025, 13(15), 2527; https://doi.org/10.3390/math13152527 - 6 Aug 2025
Viewed by 132
Abstract
This paper presents a combined theoretical, numerical, and experimental analysis to investigate the lateral plastic crushing behavior and energy absorption of circular and non-circular thin-walled rings between two rigid plates. Theoretical solutions incorporating both linear material hardening and power-law material hardening models are [...] Read more.
This paper presents a combined theoretical, numerical, and experimental analysis to investigate the lateral plastic crushing behavior and energy absorption of circular and non-circular thin-walled rings between two rigid plates. Theoretical solutions incorporating both linear material hardening and power-law material hardening models are solved via numerical shooting methods. The theoretically predicted force-denting displacement relations agree excellently with both FEA and experimental results. The FEA simulation clearly reveals the coexistence of an upper moving plastic region and a fixed bottom plastic region. A robust automatic extraction method of the fully plastic region at the bottom from FEA is proposed. A modified criterion considering the unloading effect based on the resultant moment of cross-section is proposed to allow accurate theoretical estimation of the fully plastic region length. The detailed study implies an abrupt and almost linear drop of the fully plastic region length after the maximum value by the proposed modified criterion, while the conventional fully plastic criterion leads to significant over-estimation of the length. Evolution patterns of the upper and lower plastic regions in FEA are clearly illustrated. Furthermore, the distribution of plastic energy dissipation is compared in the bottom and upper regions through FEA and theoretical results. Purely analytical solutions are formulated for linear hardening material case by elliptical integrals. A simple algebraic function solution is derived without necessity of solving differential equations for general power-law hardening material case by adopting a constant curvature assumption. Parametric analyses indicate the significant effect of ovality and hardening on plastic region evolution and crushing force. This paper should enhance the understanding of the crushing behavior of circular and non-circular rings applicable to the structural engineering and impact of the absorption domain. Full article
(This article belongs to the Special Issue Numerical Modeling and Applications in Mechanical Engineering)
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27 pages, 4506 KiB  
Article
Interpretable Machine Learning Framework for Corporate Financialization Prediction: A SHAP-Based Analysis of High-Dimensional Data
by Yanhe Wang, Wei Wei, Zhuodong Liu, Jiahe Liu, Yinzhen Lv and Xiangyu Li
Mathematics 2025, 13(15), 2526; https://doi.org/10.3390/math13152526 - 6 Aug 2025
Viewed by 368
Abstract
High-dimensional prediction problems with complex non-linear feature interactions present significant algorithmic challenges in machine learning, particularly when dealing with imbalanced datasets and multicollinearity issues. This study proposes an innovative Shapley Additive Explanations (SHAP)-enhanced machine learning framework that integrates SHAP with advanced ensemble methods [...] Read more.
High-dimensional prediction problems with complex non-linear feature interactions present significant algorithmic challenges in machine learning, particularly when dealing with imbalanced datasets and multicollinearity issues. This study proposes an innovative Shapley Additive Explanations (SHAP)-enhanced machine learning framework that integrates SHAP with advanced ensemble methods for interpretable financialization prediction. The methodology simultaneously addresses high-dimensional feature selection using 40 independent variables (19 CSR-related and 21 financialization-related), multicollinearity issues, and model interpretability requirements. Using a comprehensive dataset of 25,642 observations from 3776 Chinese A-share companies (2011–2022), we implement nine optimized machine learning algorithms with hyperparameter tuning via the Hippopotamus Optimization algorithm and five-fold cross-validation. XGBoost demonstrates superior performance with 99.34% explained variance, achieving an RMSE of 0.082 and R2 of 0.299. SHAP analysis reveals non-linear U-shaped relationships between key predictors and financialization outcomes, with critical thresholds at approximately 10 for CSR_SocR, 1.5 for CSR_S, and 5 for CSR_CV. SOE status, EPU, ownership concentration, firm size, and housing prices emerge as the most influential predictors. Notable shifts in factor importance occur during the COVID-19 pandemic period (2020–2022). This work contributes a scalable, interpretable machine learning architecture for high-dimensional financial prediction problems, with applications in risk assessment, portfolio optimization, and regulatory monitoring systems. Full article
(This article belongs to the Special Issue Advances in Artificial Intelligence, Machine Learning and Optimization)
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15 pages, 1967 KiB  
Article
Extension Distance-Driven K-Means: A Novel Clustering Framework for Fan-Shaped Data Distributions
by Xingsen Li, Hanqi Yue, Yaocong Qin and Haolan Zhang
Mathematics 2025, 13(15), 2525; https://doi.org/10.3390/math13152525 - 6 Aug 2025
Viewed by 169
Abstract
The K-means algorithm utilizes the Euclidean distance metric to quantify the similarity between data points and clusters, with the fundamental objective of assessing the relationship between points. It is important to note that, during the process of clustering, the relationships between the remaining [...] Read more.
The K-means algorithm utilizes the Euclidean distance metric to quantify the similarity between data points and clusters, with the fundamental objective of assessing the relationship between points. It is important to note that, during the process of clustering, the relationships between the remaining points in the cluster and the points to be measured are ignored. In consideration of the aforementioned issues, this paper proposes the utilization of extension distance for the purpose of evaluating the relationship between the points to be measured and the cluster classes. Furthermore, it introduces a variant of the K-means algorithm based on the separator distance. Through a series of comparative experiments, the effectiveness of the proposed algorithm for clustering fan-shaped datasets is preliminarily verified. Full article
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11 pages, 1039 KiB  
Article
A Random Riemann–Liouville Integral Operator
by Jorge Sanchez-Ortiz, Omar U. Lopez-Cresencio, Martin P. Arciga-Alejandre and Francisco J. Ariza-Hernandez
Mathematics 2025, 13(15), 2524; https://doi.org/10.3390/math13152524 - 6 Aug 2025
Viewed by 170
Abstract
In this work, we propose a definition of the random fractional Riemann–Liouville integral operator, where the order of integration is given by a random variable. Within the framework of random operator theory, we study this integral with a random kernel and establish results [...] Read more.
In this work, we propose a definition of the random fractional Riemann–Liouville integral operator, where the order of integration is given by a random variable. Within the framework of random operator theory, we study this integral with a random kernel and establish results on the measurability of the random Riemann–Liouville integral operator, which we show to be a random endomorphism of L1[a,b]. Additionally, we derive the semigroup property for these operators as a probabilistic version of the constant-order Riemann–Liouville integral. To illustrate the behavior of this operator, we present two examples involving different random variables acting on specific functions. The sample trajectories and estimated probability density functions of the resulting random integrals are then explored via Monte Carlo simulation. Full article
(This article belongs to the Special Issue Fractional Calculus and Fractional Differential Equations: Theory and Applications)
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18 pages, 484 KiB  
Article
LLM-Guided Ensemble Learning for Contextual Bandits with Copula and Gaussian Process Models
by Jong-Min Kim
Mathematics 2025, 13(15), 2523; https://doi.org/10.3390/math13152523 - 6 Aug 2025
Viewed by 337
Abstract
Contextual multi-armed bandits (CMABs) are vital for sequential decision-making in areas such as recommendation systems, clinical trials, and finance. We propose a simulation framework integrating Gaussian Process (GP)-based CMABs with vine copulas to model dependent contexts and GARCH processes to capture reward volatility. [...] Read more.
Contextual multi-armed bandits (CMABs) are vital for sequential decision-making in areas such as recommendation systems, clinical trials, and finance. We propose a simulation framework integrating Gaussian Process (GP)-based CMABs with vine copulas to model dependent contexts and GARCH processes to capture reward volatility. Rewards are generated via copula-transformed Beta distributions to reflect complex joint dependencies and skewness. We evaluate four policies—ensemble, Epsilon-greedy, Thompson, and Upper Confidence Bound (UCB)—over 10,000 replications, assessing cumulative regret, observed reward, and cumulative reward. While Thompson sampling and LLM-guided policies consistently minimize regret and maximize rewards under varied reward distributions, Epsilon-greedy shows instability, and UCB exhibits moderate performance. Enhancing the ensemble with copula features, GP models, and dynamic policy selection driven by a large language model (LLM) yields superior adaptability and performance. Our results highlight the effectiveness of combining structured probabilistic models with LLM-based guidance for robust, adaptive decision-making in skewed, high-variance environments. Full article
(This article belongs to the Special Issue Privacy-Preserving Machine Learning in Large Language Models (LLMs))
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32 pages, 2173 KiB  
Article
A Swarm-Based Multi-Objective Framework for Lightweight and Real-Time IoT Intrusion Detection
by Hessah A. Alsalamah and Walaa N. Ismail
Mathematics 2025, 13(15), 2522; https://doi.org/10.3390/math13152522 - 5 Aug 2025
Viewed by 240
Abstract
Internet of Things (IoT) applications and services have transformed the way people interact with their environment, enhancing comfort and quality of life. Additionally, Machine Learning (ML) approaches show significant promise for detecting intrusions in IoT environments. However, the high dimensionality, class imbalance, and [...] Read more.
Internet of Things (IoT) applications and services have transformed the way people interact with their environment, enhancing comfort and quality of life. Additionally, Machine Learning (ML) approaches show significant promise for detecting intrusions in IoT environments. However, the high dimensionality, class imbalance, and complexity of network traffic—combined with the dynamic nature of sensor networks—pose substantial challenges to the development of efficient and effective detection algorithms. In this study, a multi-objective metaheuristic optimization approach, referred to as MOOIDS-IoT, is integrated with ML techniques to develop an intelligent cybersecurity system for IoT environments. MOOIDS-IoT combines a Genetic Algorithm (GA)-based feature selection technique with a multi-objective Particle Swarm Optimization (PSO) algorithm. PSO optimizes convergence speed, model complexity, and classification accuracy by dynamically adjusting the weights and thresholds of the deployed classifiers. Furthermore, PSO integrates Pareto-based multi-objective optimization directly into the particle swarm framework, extending conventional swarm intelligence while preserving a diverse set of non-dominated solutions. In addition, the GA reduces training time and eliminates redundancy by identifying the most significant input characteristics. The MOOIDS-IoT framework is evaluated using two lightweight models—MOO-PSO-XGBoost and MOO-PSO-RF—across two benchmark datasets, namely the NSL-KDD and CICIoT2023 datasets. On CICIoT2023, MOO-PSO-RF obtains 91.42% accuracy, whereas MOO-PSO-XGBoost obtains 98.38% accuracy. In addition, both models perform well on NSL-KDD (MOO-PSO-RF: 99.66% accuracy, MOO-PSO-XGBoost: 98.46% accuracy). The proposed approach is particularly appropriate for IoT applications with limited resources, where scalability and model efficiency are crucial considerations. Full article
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15 pages, 1839 KiB  
Article
Cluster Complementarity and Consistency Mining for Multi-View Representation Learning
by Yanyan Wen and Haifeng Li
Mathematics 2025, 13(15), 2521; https://doi.org/10.3390/math13152521 - 5 Aug 2025
Viewed by 194
Abstract
With the advent of the big data era, multi-view clustering (MVC) methods have attracted considerable acclaim due to their capability in handling the multifaceted nature of data, which achieves impressive results across various fields. However, two significant challenges persist in MVC methods: (1) [...] Read more.
With the advent of the big data era, multi-view clustering (MVC) methods have attracted considerable acclaim due to their capability in handling the multifaceted nature of data, which achieves impressive results across various fields. However, two significant challenges persist in MVC methods: (1) They resort to learning view-invariant information of samples to bridge the heterogeneity gap between views, which may result in the loss of view-specific information that contributes to pattern mining. (2) They utilize fusion strategies that are susceptible to the discriminability of views, i.e., the concatenation and the weighing fusion of cross-view representations, to aggregate complementary and consistent information, which is difficult to guarantee semantic robustness of fusion representations. To this end, a simple yet effective cluster complementarity and consistency learning framework (CommonMVC) is proposed for mining patterns of multiview data. Specifically, a cluster complementarity learning is devised to endow fusion representations with discriminate information via nonlinearly aggregating view-specific information. Meanwhile, a cluster consistency learning is introduced via modeling instance-level and cluster-level partition invariance to coordinate the clustering partition of various views, which ensures the robustness of multi-view data pattern mining. Seamless collaboration between two components effectively enhances multi-view clustering performance. Finally, comprehensive experiments on four real-world datasets demonstrate CommonMVC establishes a new state-of-the-art baseline for the MVC task. Full article
(This article belongs to the Special Issue Artificial Intelligence and Data Science, 2nd Edition)
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14 pages, 301 KiB  
Article
Oscillatory Analysis of Third-Order Hybrid Trinomial Delay Differential Equations via Binomial Transform
by Ganesh Purushothaman, Ekambaram Chandrasekaran, George E. Chatzarakis and Ethiraju Thandapani
Mathematics 2025, 13(15), 2520; https://doi.org/10.3390/math13152520 - 5 Aug 2025
Viewed by 162
Abstract
The oscillatory behavior of a class of third-order hybrid-type delay differential equations—used to model various real-world phenomena in fluid dynamics, control systems, biology, and beam deflection—is investigated in this study. A novel method is proposed, whereby these complex trinomial equations are reduced to [...] Read more.
The oscillatory behavior of a class of third-order hybrid-type delay differential equations—used to model various real-world phenomena in fluid dynamics, control systems, biology, and beam deflection—is investigated in this study. A novel method is proposed, whereby these complex trinomial equations are reduced to a simpler binomial form by employing solutions of the corresponding linear differential equations. Through the use of comparison techniques and integral averaging methods, new oscillation criteria are derived to ensure that all solutions exhibit oscillatory behavior. These results are shown to extend and enhance existing theories in the oscillation analysis of functional differential equations. The effectiveness and originality of the proposed approach are illustrated by means of two representative examples. Full article
(This article belongs to the Section C1: Difference and Differential Equations)
11 pages, 324 KiB  
Article
Controller Design for Continuous-Time Linear Control Systems with Time-Varying Delay
by Hongli Yang, Lijuan Yang and Ivan Ganchev Ivanov
Mathematics 2025, 13(15), 2519; https://doi.org/10.3390/math13152519 - 5 Aug 2025
Viewed by 209
Abstract
This paper addresses the controller design problem for linear systems with time-varying delays. By constructing a novel Lyapunov–Krasovskii functional incorporating delay-partitioning techniques, we establish delay-dependent stability criteria for the solvability of the robust stabilization problem. The derived conditions are formulated as linear matrix [...] Read more.
This paper addresses the controller design problem for linear systems with time-varying delays. By constructing a novel Lyapunov–Krasovskii functional incorporating delay-partitioning techniques, we establish delay-dependent stability criteria for the solvability of the robust stabilization problem. The derived conditions are formulated as linear matrix inequalities (LMIs) that become affine upon fixing a single scalar parameter, thereby facilitating efficient numerical computation. Furthermore, these criteria guarantee that the reachable set of the closed-loop system remains bounded within a prescribed ellipsoid under zero initial conditions. The effectiveness and superiority of the proposed approach are demonstrated through two comparative numerical examples, including a benchmark problem with varying delay. Full article
(This article belongs to the Special Issue Control Theory and Applications, 2nd Edition)
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34 pages, 2291 KiB  
Article
A Study of Periodicities in a One-Dimensional Piecewise Smooth Discontinuous Map
by Rajanikant A. Metri, Bhooshan Rajpathak, Kethavath Raghavendra Naik and Mohan Lal Kolhe
Mathematics 2025, 13(15), 2518; https://doi.org/10.3390/math13152518 - 5 Aug 2025
Viewed by 312
Abstract
In this study, we investigate the nonlinear dynamical behavior of a one-dimensional linear piecewise-smooth discontinuous (LPSD) map with a negative slope, motivated by its occurrence in systems exhibiting discontinuities, such as power electronic converters. The objective of the proposed research is to develop [...] Read more.
In this study, we investigate the nonlinear dynamical behavior of a one-dimensional linear piecewise-smooth discontinuous (LPSD) map with a negative slope, motivated by its occurrence in systems exhibiting discontinuities, such as power electronic converters. The objective of the proposed research is to develop an analytical approach. Analytical conditions are derived for the existence of stable period-1 and period-2 orbits within the third quadrant of the parameter space defined by slope coefficients a<0 and b<0. The coexistence of multiple attractors is demonstrated. We also show that a novel class of orbits exists in which both points lie entirely in either the left or right domain. These orbits are shown to eventually exhibit periodic behavior, and a closed-form expression is derived to compute the number of iterations required for a trajectory to converge to such orbits. This method also enhances the ease of analyzing system stability by mapping the state–variable dynamics using a non-smooth discontinuous map. The analytical findings are validated using bifurcation diagrams, cobweb plots, and basin of attraction visualizations. Full article
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28 pages, 3266 KiB  
Article
Wavelet Multiresolution Analysis-Based Takagi–Sugeno–Kang Model, with a Projection Step and Surrogate Feature Selection for Spectral Wave Height Prediction
by Panagiotis Korkidis and Anastasios Dounis
Mathematics 2025, 13(15), 2517; https://doi.org/10.3390/math13152517 - 5 Aug 2025
Viewed by 136
Abstract
The accurate prediction of significant wave height presents a complex yet vital challenge in the fields of ocean engineering. This capability is essential for disaster prevention, fostering sustainable development and deepening our understanding of various scientific phenomena. We explore the development of a [...] Read more.
The accurate prediction of significant wave height presents a complex yet vital challenge in the fields of ocean engineering. This capability is essential for disaster prevention, fostering sustainable development and deepening our understanding of various scientific phenomena. We explore the development of a comprehensive predictive methodology for wave height prediction by integrating novel Takagi–Sugeno–Kang fuzzy models within a multiresolution analysis framework. The multiresolution analysis emerges via wavelets, since they are prominent models characterised by their inherent multiresolution nature. The maximal overlap discrete wavelet transform is utilised to generate the detail and resolution components of the time series, resulting from this multiresolution analysis. The novelty of the proposed model lies on its hybrid training approach, which combines least squares with AdaBound, a gradient-based algorithm derived from the deep learning literature. Significant wave height prediction is studied as a time series problem, hence, the appropriate inputs to the model are selected by developing a surrogate-based wrapped algorithm. The developed wrapper-based algorithm, employs Bayesian optimisation to deliver a fast and accurate method for feature selection. In addition, we introduce a projection step, to further refine the approximation capabilities of the resulting predictive system. The proposed methodology is applied to a real-world time series pertaining to spectral wave height and obtained from the Poseidon operational oceanography system at the Institute of Oceanography, part of the Hellenic Center for Marine Research. Numerical studies showcase a high degree of approximation performance. The predictive scheme with the projection step yields a coefficient of determination of 0.9991, indicating a high level of accuracy. Furthermore, it outperforms the second-best comparative model by approximately 49% in terms of root mean squared error. Comparative evaluations against powerful artificial intelligence models, using regression metrics and hypothesis test, underscore the effectiveness of the proposed methodology. Full article
(This article belongs to the Special Issue Applications of Mathematics in Neural Networks and Machine Learning)
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23 pages, 2235 KiB  
Article
Ternary Historical Memory-Based Robust Clustered Particle Swarm Optimization for Dynamic Berth Allocation and Crane Assignment Problem
by Ruiqi Wu, Shiming Mao and Yi Sun
Mathematics 2025, 13(15), 2516; https://doi.org/10.3390/math13152516 - 5 Aug 2025
Viewed by 201
Abstract
The berth allocation and crane assignment problem (BACAP) is a key challenge in port logistics, particularly under dynamic and uncertain vessel arrival conditions. To address the limitations of existing methods in handling large-scale and high-disturbance scenarios, this paper proposes a novel optimization framework: [...] Read more.
The berth allocation and crane assignment problem (BACAP) is a key challenge in port logistics, particularly under dynamic and uncertain vessel arrival conditions. To address the limitations of existing methods in handling large-scale and high-disturbance scenarios, this paper proposes a novel optimization framework: Ternary Historical Memory-based Robust Clustered Particle Swarm Optimization (THM-RCPSO). In this method, the initial particle swarm is divided into multiple clusters, each conducting local searches to identify regional optima. These clusters then exchange information to iteratively refine the global best solution. A ternary historical memory mechanism further enhances the optimization by recording and comparing the best solutions from three different strategies, ensuring guidance from historical performance during exploration. Experimental evaluations on 25 dynamic BACAP benchmark instances show that THM-RCPSO achieves the lowest average vessel dwell time in 22 out of 25 cases, with the lowest overall average rank among five tested algorithms. Specifically, it demonstrates significant advantages on large-scale instances with 150 vessels, where it consistently outperforms competing methods such as HRBA, ACO, and GAMCS in both solution quality and robustness. These results confirm THM-RCPSO’s strong capability in solving dynamic and large-scale DBACAP scenarios with high disturbance levels. Full article
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15 pages, 287 KiB  
Article
Analytical Pricing Vulnerable Options with Stochastic Volatility in a Two-Factor Stochastic Interest Rate Model
by Junkee Jeon and Geonwoo Kim
Mathematics 2025, 13(15), 2515; https://doi.org/10.3390/math13152515 - 5 Aug 2025
Viewed by 190
Abstract
This paper develops an analytical pricing formula for vulnerable options with stochastic volatility under a two-factor stochastic interest rate model. We consider the underlying asset price following the Heston stochastic volatility model, while the interest rate is modeled as the sum of two [...] Read more.
This paper develops an analytical pricing formula for vulnerable options with stochastic volatility under a two-factor stochastic interest rate model. We consider the underlying asset price following the Heston stochastic volatility model, while the interest rate is modeled as the sum of two processes. Using the joint characteristic function approach and measure change techniques, we derive an explicit pricing formula for a vulnerable European option. We also conduct numerical experiments to examine the effects of various model parameters on option values. This study provides a more realistic framework for pricing OTC derivatives by incorporating credit risk, stochastic volatility, and stochastic interest rates simultaneously. Full article
(This article belongs to the Special Issue Mathematical Finance: Statistical Inference, Stochastic Modeling, and Advanced Algorithms)
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15 pages, 262 KiB  
Article
Uniqueness of Solution for Impulsive Evolution Equation in Ordered Banach Spaces
by Weifeng Ma and Yongxiang Li
Mathematics 2025, 13(15), 2514; https://doi.org/10.3390/math13152514 - 5 Aug 2025
Viewed by 168
Abstract
This paper investigates the periodic boundary value problem for impulsive evolution equation in ordered Banach space. By applying the Poincaré mapping and monotone iterative method, we obtain the existence results of mild solutions and positive mild solutions for impulsive evolution equation. Further, we [...] Read more.
This paper investigates the periodic boundary value problem for impulsive evolution equation in ordered Banach space. By applying the Poincaré mapping and monotone iterative method, we obtain the existence results of mild solutions and positive mild solutions for impulsive evolution equation. Further, we obtain the uniqueness of mild solution. Full article
18 pages, 861 KiB  
Article
Observer-Based Exponential Stability Control of T-S Fuzzy Networked Systems with Varying Communication Delays
by Hejun Yao and Fangzheng Gao
Mathematics 2025, 13(15), 2513; https://doi.org/10.3390/math13152513 - 5 Aug 2025
Viewed by 142
Abstract
This paper is concerned with the problem of dynamic output feedback exponential stability control of T-S fuzzy networked control systems (NCSs) with varying communication delays. First, with consideration of varying communication delays, a new model of the networked systems is established by using [...] Read more.
This paper is concerned with the problem of dynamic output feedback exponential stability control of T-S fuzzy networked control systems (NCSs) with varying communication delays. First, with consideration of varying communication delays, a new model of the networked systems is established by using the T-S fuzzy method, and a state observer is designed to estimate the unknown control disturbance. Then, a delay-dependent exponential stability criterion of closed-loop systems is derived by means of iterative technique and multiple augmented Lyapnov functionals and the linear matrix inequality (LMI) method. Furthermore, an observer-based controller is explicitly constructed to realize exponential stability control for this class of NCSs. An iterative algorithm is developed to compute the controller’s matrix by means of the Cone Complementarity Linearization Method (CCLM). Lastly, the validity and feasibility of the proposed exponential stability criterion are confirmed via a numerical simulation example. Full article
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1 pages, 127 KiB  
Correction
Correction: Bai et al. A Study on q-Starlike Functions Connected with q-Extension of Hyperbolic Secant and Janowski Functions. Mathematics 2025, 13, 2173
by Pengfei Bai, Adeel Ahmad, Akhter Rasheed, Saqib Hussain, Huo Tang and Saima Noor
Mathematics 2025, 13(15), 2512; https://doi.org/10.3390/math13152512 - 5 Aug 2025
Viewed by 114
Abstract
In the original publication [...] Full article
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