Processing math: 100%
Previous Issue
Volume 13, April-2
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.0
2.3
Journals
Mathematics
Volume 13
Issue 9
share announcement

Mathematics, Volume 13, Issue 9 (May-1 2025) – 174 articles

  • Issues are regarded as officially published after their release is announced to the table of contents alert mailing list.
  • You may sign up for e-mail alerts to receive table of contents of newly released issues.
  • PDF is the official format for papers published in both, html and pdf forms. To view the papers in pdf format, click on the "PDF Full-text" link, and use the free Adobe Reader to open them.
Order results
Result details
Section
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
13 pages, 2179 KiB  
Article
Semi-Supervised Clustering via Constraints Self-Learning
by Xin Sun
Mathematics 2025, 13(9), 1535; https://doi.org/10.3390/math13091535 (registering DOI) - 7 May 2025
Abstract
So far, most of the semi-supervised clustering algorithms focus on finding a suitable partition that well satisfies the given constraints. However, insufficient supervisory information may lead to over-fitting results and unstable performance, especially on complicated data. To address this challenge, this paper attempts [...] Read more.
So far, most of the semi-supervised clustering algorithms focus on finding a suitable partition that well satisfies the given constraints. However, insufficient supervisory information may lead to over-fitting results and unstable performance, especially on complicated data. To address this challenge, this paper attempts to solve the semi-supervised clustering problem by self-learning sufficient constraints. The essential motivation is that constraints can be learned from the local neighbor structures within appropriate feature spaces, and sufficient constraints can directly divide the data into clusters. Hence, we first present a constraint self-learning framework. It performs an expectation–maximization procedure iteratively between exploring a discriminant space and learning new constraints. Then, a constraint-based clustering algorithm is proposed by taking advantage of sufficient constraints. Experimental studies on various real-world benchmark datasets show that the proposed algorithm achieves promising performance and outperforms the state-of-the-art semi-supervised clustering algorithms. Full article
(This article belongs to the Special Issue Artificial Intelligence Applications with Advanced Mathematical Methods)
►▼ Show Figures

Figure 1

19 pages, 1196 KiB  
Article
Fixed-Time Event-Triggered Consensus Power-Sharing Control for Hybrid AC/DC Microgrid Parallel Bi-Directional Interconnect Converters
by Junjie Wu, Siyu Lyu, Benhua Qian, Chuanyu Jiang, Ziqaing Song and Jun Xiao
Mathematics 2025, 13(9), 1534; https://doi.org/10.3390/math13091534 (registering DOI) - 7 May 2025
Abstract
Although power sharing in hybrid AC/DC microgrids (HMGs) has been widely researched, traditional power-sharing control is based on an infinite time consensus method, and the communication bandwidth is large. Therefore, this paper proposes a power-sharing strategy for HMG parallel bi-directional interconnected converters (BICs) [...] Read more.
Although power sharing in hybrid AC/DC microgrids (HMGs) has been widely researched, traditional power-sharing control is based on an infinite time consensus method, and the communication bandwidth is large. Therefore, this paper proposes a power-sharing strategy for HMG parallel bi-directional interconnected converters (BICs) considering fixed-time stabilization and event-triggered control. Firstly, every BIC has a well-designed local control method to generate the corresponding power reference for the BIC, which provides the basis for further research. Secondly, a fixed-time-based power-sharing controller is designed in order to improve the convergence speed of power-sharing control for HMG parallel BICs. Finally, an event-triggered method is applied to reduce the system communication bandwidth and the frequency of controller updates. In this paper, we first transform the parallel BIC control problem into a multi-agent system (MAS) consensus problem. Furthermore, a fixed time based on an event trigger consensus method is proposed at the secondary control level. The energy flow between the two subgrids can be shared according to the rated power of each BIC. Finally, the effectiveness of the proposed fixed-time event-triggered power-sharing control is verified through simulation and experiments. Full article
►▼ Show Figures

Figure 1

20 pages, 918 KiB  
Article
The Linear Stability of a Power-Law Liquid Film Flowing Down an Inclined Deformable Plane
by Karim Ladjelate, Nadia Mehidi Bouam, Amar Djema, Abdelkader Belhenniche and Roman Chertovskih
Mathematics 2025, 13(9), 1533; https://doi.org/10.3390/math13091533 - 7 May 2025
Abstract
A linear stability analysis is performed for a power-law liquid film flowing down an inclined rigid plane over a deformable solid layer. The deformable solid is modeled using a neo-Hookean constitutive equation, characterized by a constant shear modulus and a nonzero first normal [...] Read more.
A linear stability analysis is performed for a power-law liquid film flowing down an inclined rigid plane over a deformable solid layer. The deformable solid is modeled using a neo-Hookean constitutive equation, characterized by a constant shear modulus and a nonzero first normal stress difference in the base state at the fluid–solid interface. To solve the linearized eigenvalue problem, the Riccati transformation method, which offers advantages over traditional techniques by avoiding the parasitic growth seen in the shooting method and eliminating the need for large-scale matrix eigenvalue computations, was used. This method enhances both analytical clarity and computational efficiency. Results show that increasing solid deformability destabilizes the flow at low Reynolds numbers by promoting short-wave modes, while its effect becomes negligible at high Reynolds numbers where inertia dominates. The fluid’s rheology also plays a key role: at low Reynolds numbers, shear-thinning fluids (n<1) are more prone to instability, whereas at high Reynolds numbers, shear-thickening fluids (n>1) exhibit a broader unstable regime. Full article
(This article belongs to the Special Issue Advances and Applications in Computational Fluid Dynamics)
►▼ Show Figures

Figure 1

13 pages, 1366 KiB  
Article
Structure Fault Tolerance of Fully Connected Cubic Networks
by Eminjan Sabir and Cheng-Kuan Lin
Mathematics 2025, 13(9), 1532; https://doi.org/10.3390/math13091532 - 7 May 2025
Abstract
An interconnection network is usually modeled by a graph, and fault tolerance of the interconnection network is often measured by connectivity of the graph. Given a connected subgraph L of a graph G and non-negative integer t, the t-extra connectivity [...] Read more.
An interconnection network is usually modeled by a graph, and fault tolerance of the interconnection network is often measured by connectivity of the graph. Given a connected subgraph L of a graph G and non-negative integer t, the t-extra connectivity κt(G), the L-structure connectivity κ(G;L) and the t-extra L-structure connectivity κg(G;L) of G can provide new metrics to measure the fault tolerance of a network represented by G. Fully connected cubic networks FCn are a class of hierarchical networks which enjoy the strengths of a constant vertex degree and good expansibility. In this paper, we determine κt(FCn), κ(FCn;L) and κt(FCn;L) for t=1 and L∈{K1,1,K1,2,K1,3}. We also establish the edge versions λt(FCn), λ(FCn;L) and λt(FCn;L) for t=1 and L∈{K1,1,K1,2}. Full article
►▼ Show Figures

Figure 1

26 pages, 7904 KiB  
Article
Sustainable PV Power Forecasting via MPA-VMD Optimized BiGRU with Attention Mechanism
by Yongmei Ding, Shangnan Zhou and Wenwu Deng
Mathematics 2025, 13(9), 1531; https://doi.org/10.3390/math13091531 - 7 May 2025
Abstract
Accurate photovoltaic (PV) power generation forecasting is crucial for optimizing grid management and enhancing the reliability of sustainable energy systems. This study creates a novel hybrid model—MPA-VMD-BiGRU-MAM—designed to improve PV power forecasting accuracy through advanced decomposition and deep learning techniques. Initially, the Kendall [...] Read more.
Accurate photovoltaic (PV) power generation forecasting is crucial for optimizing grid management and enhancing the reliability of sustainable energy systems. This study creates a novel hybrid model—MPA-VMD-BiGRU-MAM—designed to improve PV power forecasting accuracy through advanced decomposition and deep learning techniques. Initially, the Kendall correlation coefficient is applied to identify key influencing factors, ensuring robust feature selection for the model inputs. The Marine Predator Algorithm (MPA) optimizes the hyperparameters of Variational Mode Decomposition (VMD), effectively segmenting the PV power time series into informative sub-modes. These sub-modes are processed using a bidirectional gated recurrent unit (BiGRU) enhanced with a multi-head attention mechanism (MAM), enabling dynamic weight assignment and comprehensive feature extraction. Empirical evaluations on PV datasets from Alice Springs, Australia, and Belgium indicate that our hybrid model consistently surpasses baseline methods and achieves a 38.34% reduction in Mean Absolute Error (MAE), a 19.6% reduction in Root Mean Square Error (RMSE), a 4.41% improvement in goodness of fit, and a 33.91% increase in stability (STA) for the Australian dataset. For the Belgian dataset, the model attains a 96.32% reduction in MAE, a 95.84% decrease in RMSE, an 11.92% enhancement in goodness of fit, and an STA of 92.08%. We demonstrate the model’s effectiveness in capturing seasonal trends and addressing the inherent variability in PV power generation, offering a reliable solution to the challenges of instability, intermittency, and unpredictability in renewable energy sources. Full article
►▼ Show Figures

Figure 1

23 pages, 495 KiB  
Article
Multi-View Graph Contrastive Neural Networks for Session-Based Recommendation
by Pengbo Huang and Chun Wang
Mathematics 2025, 13(9), 1530; https://doi.org/10.3390/math13091530 - 6 May 2025
Abstract
Session-based recommendation (SBR) aims to predict the next item a user may interact with based on an anonymous session, playing a crucial role in real-time recommendation scenarios. However, existing SBR models struggle to effectively capture local session dependencies and global item relationships, while [...] Read more.
Session-based recommendation (SBR) aims to predict the next item a user may interact with based on an anonymous session, playing a crucial role in real-time recommendation scenarios. However, existing SBR models struggle to effectively capture local session dependencies and global item relationships, while also facing challenges such as data sparsity and noisy information interference. To address these challenges, this paper proposes a novel Multi-View Graph Contrastive Learning Neural Network (MVGCL-GNN), which enhances recommendation performance through multi-view graph modeling and contrastive learning. Specifically, we construct three key graph structures: a session graph for modeling short-term item dependencies, a global item graph for capturing cross-session item transitions, and a global category graph for learning category-level relationships. In addition, we introduce simple graph contrastive learning to improve embedding quality and reduce noise interference. Furthermore, a soft attention mechanism is employed to effectively integrate session-level and global-level information representations. Extensive experiments conducted on two real-world datasets demonstrate that MVGCL-GNN consistently outperforms state-of-the-art baselines. MVGCL-GNN achieves 34.96% in P@20 and 16.50% in MRR@20 on the Tmall dataset, and 22.59% in P@20 and 8.60% in MRR@20 on the Nowplaying dataset. These results validate the effectiveness of multi-view graphs and contrastive learning in improving both accuracy and robustness for session-based recommendation tasks. Full article
(This article belongs to the Special Issue Advanced Image Processing and Computational Intelligence: Methodologies and Applications)
►▼ Show Figures

Figure 1

25 pages, 1130 KiB  
Article
Multi-Domain Controversial Text Detection Based on a Machine Learning and Deep Learning Stacked Ensemble
by Jiadi Liu, Zhuodong Liu, Qiaoqi Li, Weihao Kong and Xiangyu Li
Mathematics 2025, 13(9), 1529; https://doi.org/10.3390/math13091529 - 6 May 2025
Abstract
Due to the rapid proliferation of social media and online reviews, the accurate identification and classification of controversial texts has emerged as a significant challenge in the field of natural language processing. However, traditional text-classification methodologies frequently encounter critical limitations, such as feature [...] Read more.
Due to the rapid proliferation of social media and online reviews, the accurate identification and classification of controversial texts has emerged as a significant challenge in the field of natural language processing. However, traditional text-classification methodologies frequently encounter critical limitations, such as feature sensitivity and inadequate generalization capabilities. This results in a notably suboptimal performance when confronted with diverse controversial content. To address these substantial limitations, this paper proposes a novel controversial text-detection framework based on stacked ensemble learning to enhance the accuracy and robustness of text classification. Firstly, considering the multidimensional complexity of textual features, we integrate comprehensive feature engineering, i.e., encompassing word frequency, statistical metrics, sentiment analysis, and comment tree structure features, as well as advanced feature selection methodologies, particularly lassonet, i.e., a neural network with feature sparsity, to effectively address dimensionality challenges while enhancing model interpretability and computational efficiency. Secondly, we design a two-tier stacked ensemble architecture, which not only combines the strengths of multiple machine learning algorithms, e.g., gradient-boosted decision tree (GBDT), random forest (RF), and extreme gradient boosting (XGBoost), with deep learning models, e.g., gated recurrent unit (GRU) and long short-term memory (LSTM), but also implements the support vector machine (SVM) for efficient meta-learning. Furthermore, we systematically compare three hyperparameter optimization algorithms, including the sparrow search algorithm (SSA), particle swarm optimization (PSO), and Bayesian optimization (BO). The experimental results demonstrate that the SSA exhibits a superior performance in exploring high-dimensional parameter spaces. Extensive experimentation across diverse topics and domains also confirms that our proposed methodology significantly outperforms the state-of-the-art approaches. Full article
(This article belongs to the Special Issue Machine Learning Methods and Mathematical Modeling with Applications)
21 pages, 2514 KiB  
Article
United Prediction of Travel Modes and Purposes in Travel Chains Based on Multitask Learning Deep Neural Networks
by Chenxi Xiao, Zhitao Li, Jinjun Tang and Jeanyoung Jay Lee
Mathematics 2025, 13(9), 1528; https://doi.org/10.3390/math13091528 - 6 May 2025
Abstract
Predicting and analyzing travel mode choices and purposes are significant to improve urban travel mobility and transportation planning. Previous research has ignored the interconnection between travel mode choices and purposes and thus overlooked their potential contributions to predictions. Using individual travel chain data [...] Read more.
Predicting and analyzing travel mode choices and purposes are significant to improve urban travel mobility and transportation planning. Previous research has ignored the interconnection between travel mode choices and purposes and thus overlooked their potential contributions to predictions. Using individual travel chain data collected in South Korea, this study proposes a Multi-Task Learning Deep Neural Network (MTLDNN) framework, integrating RFM (Recency, Frequency, Monetary) to achieve a joint prediction of travel mode choices and purposes. The MTLDNN is constructed to share a common hidden layer that extracts general features from the input data, while task-specific output layers are dedicated to predicting travel modes and purposes separately. This structure allows for efficient learning of shared representations while maintaining the capacity to model task-specific relationships. RFM is then integrated to optimize the extraction of users’ behavioral features, which helps in better understanding the temporal and financial patterns of users’ travel activities. The results show that the MTLDNN demonstrates consistent input variable replacement modes and selection probabilities in generating behavioral replacement patterns. Compared to the multinomial logit model (MNL), the MTLDNN achieves lower cross-entropy loss and higher prediction accuracy. The proposed framework could enhance transportation planning, efficiency, and user satisfaction by enabling more accurate predictions. Full article
►▼ Show Figures

Figure 1

17 pages, 467 KiB  
Article
Multivariate Extension Application for Spearman’s Footrule Correlation Coefficient
by Liqi Xia, Sami Ullah and Li Guan
Mathematics 2025, 13(9), 1527; https://doi.org/10.3390/math13091527 - 6 May 2025
Abstract
This paper presents a simplified and computationally feasible multivariate extension. A correlation matrix is constructed using pairwise Spearman’s footrule correlation coefficients, and these coefficients are shown to jointly converge to a multivariate normal distribution. A global test statistic based on the Frobenius norm [...] Read more.
This paper presents a simplified and computationally feasible multivariate extension. A correlation matrix is constructed using pairwise Spearman’s footrule correlation coefficients, and these coefficients are shown to jointly converge to a multivariate normal distribution. A global test statistic based on the Frobenius norm of this matrix asymptotically follows a weighted sum of chi-square distributions. Simulation studies and two real-world applications (a sensory analysis of French Jura wines and the characterization of plant leaf specimens) demonstrate the practical utility of the proposed method, bridging the gap between theoretical rigor and practical implementation in multivariate nonparametric inference. Full article
►▼ Show Figures

Figure 1

22 pages, 881 KiB  
Article
On the Special Viviani’s Curve and Its Corresponding Smarandache Curves
by Yangke Deng, Yanlin Li, Süleyman Şenyurt, Davut Canlı and İremnur Gürler
Mathematics 2025, 13(9), 1526; https://doi.org/10.3390/math13091526 - 6 May 2025
Abstract
In the present paper, the special Viviani’s curve is revisited in the context of Smarandache geometry. Accordingly, the paper first defines the special Smarandache curves of Viviani’s curve, including the Darboux vector. Then, it expresses the resulting Frenet apparatus for each Smarandache curve [...] Read more.
In the present paper, the special Viviani’s curve is revisited in the context of Smarandache geometry. Accordingly, the paper first defines the special Smarandache curves of Viviani’s curve, including the Darboux vector. Then, it expresses the resulting Frenet apparatus for each Smarandache curve in terms of the Viviani’s curve. The paper is also supported by extensive graphical representations of Viviani’s curve and its Smarandache curves, as well as their respective curvatures. Full article
(This article belongs to the Special Issue Submanifolds in Metric Manifolds, 2nd Edition)
22 pages, 387 KiB  
Article
Sufficient Conditions for Optimal Stability in Hilfer–Hadamard Fractional Differential Equations
by Safoura Rezaei Aderyani, Reza Saadati and Donal O’Regan
Mathematics 2025, 13(9), 1525; https://doi.org/10.3390/math13091525 - 6 May 2025
Abstract
The primary objective of this study is to explore sufficient conditions for the existence, uniqueness, and optimal stability of positive solutions to a finite system of Hilfer–Hadamard fractional differential equations with two-point boundary conditions. Our analysis centers around transforming fractional differential equations into [...] Read more.
The primary objective of this study is to explore sufficient conditions for the existence, uniqueness, and optimal stability of positive solutions to a finite system of Hilfer–Hadamard fractional differential equations with two-point boundary conditions. Our analysis centers around transforming fractional differential equations into fractional integral equations under minimal requirements. This investigation employs several well-known special control functions, including the Mittag–Leffler function, the Wright function, and the hypergeometric function. The results are obtained by constructing upper and lower control functions for nonlinear expressions without any monotonous conditions, utilizing fixed point theorems, such as Banach and Schauder, and applying techniques from nonlinear functional analysis. To demonstrate the practical implications of the theoretical findings, a pertinent example is provided, which validates the results obtained. Full article
(This article belongs to the Special Issue Current Topics in Optimization, Inequalities and Convex Function Theory)
►▼ Show Figures

Figure 1

26 pages, 5898 KiB  
Article
Thermophysical Properties and Expectation Values for Pöschl–Teller-like Pseudo-Harmonic Oscillator
by Haifa I. Alrebdi, Uduakobong S. Okorie, Ridha Horchani, Gaotsiwe J. Rampho and Akpan N. Ikot
Mathematics 2025, 13(9), 1524; https://doi.org/10.3390/math13091524 - 6 May 2025
Abstract
The Nikiforov–Uvarov functional analysis (NUFA) formalism is employed to study approximately the eigensolutions of the Schrodinger equation with the Pöschl–Teller-like pseudo-harmonic oscillator (PTPO). The variations in the energy spectra and the wave functions as a function of the screening parameters for different quantum [...] Read more.
The Nikiforov–Uvarov functional analysis (NUFA) formalism is employed to study approximately the eigensolutions of the Schrodinger equation with the Pöschl–Teller-like pseudo-harmonic oscillator (PTPO). The variations in the energy spectra and the wave functions as a function of the screening parameters for different quantum states were investigated. With the energy expression of PTPO, the partition function and other thermodynamic function were obtained as a function of temperature for different values of the screening parameters using the Euler–Maclaurin formula. Using the Hellmann–Feynman theorem (HFT), we evaluate the expectation values of PTPO numerically and graphically for various values of the screening parameters and quantum states. It is observed that the eigensolutions, thermodynamic functions and expectation values of PTPO system are influenced by quantum states, screening parameters and temperature. Full article
►▼ Show Figures

Figure 1

19 pages, 9204 KiB  
Article
Numerical Study of Salt Ion Transport in Electromembrane Systems with Ion-Exchange Membranes Having Geometrically Structured Surfaces
by Evgenia Kirillova, Natalia Chubyr, Anna Kovalenko and Mahamet Urtenov
Mathematics 2025, 13(9), 1523; https://doi.org/10.3390/math13091523 - 6 May 2025
Abstract
This article is devoted to numerically modeling the effect of the geometric modification of the surfaces of ion-exchange membranes in electromembrane systems (EMSs) on the salt ion transport using a 2D mathematical model of the transport process in the desalination channel based on [...] Read more.
This article is devoted to numerically modeling the effect of the geometric modification of the surfaces of ion-exchange membranes in electromembrane systems (EMSs) on the salt ion transport using a 2D mathematical model of the transport process in the desalination channel based on boundary value problems for the coupled system of Nernst–Planck–Poisson and Navier–Stokes equations. The main patterns of salt ion transport are established taking into account diffusion, electromigration, forced convection, electroconvection, and the geometric modification of the surface of ion-exchange membranes. It is shown that the geometric modification of the surface of ion-exchange membranes significantly changes both the formation and development of electroconvection. A significant combined effect of electroconvection and geometric modification of the surface of ion-exchange membranes in the desalination channel on the salt ion transport is shown, as well as a complex, nonlinear, and non-stationary interaction of all the main effects of concentration polarization in the desalination channel. Full article
(This article belongs to the Special Issue Mathematical Applications in Electrical Engineering, 2nd Edition)
►▼ Show Figures

Figure 1

28 pages, 1418 KiB  
Article
Variable Selection for Additive Quantile Regression with Nonlinear Interaction Structures
by Yongxin Bai, Jiancheng Jiang and Maozai Tian
Mathematics 2025, 13(9), 1522; https://doi.org/10.3390/math13091522 - 5 May 2025
Viewed by 40
Abstract
In high-dimensional data analysis, main effects and interaction effects often coexist, especially when complex nonlinear relationships are present. Effective variable selection is crucial for avoiding the curse of dimensionality and enhancing the predictive performance of a model. In this paper, we introduce a [...] Read more.
In high-dimensional data analysis, main effects and interaction effects often coexist, especially when complex nonlinear relationships are present. Effective variable selection is crucial for avoiding the curse of dimensionality and enhancing the predictive performance of a model. In this paper, we introduce a nonlinear interaction structure into the additive quantile regression model and propose an innovative penalization method. This method considers the complexity and smoothness of the additive model and incorporates heredity constraints on main effects and interaction effects through an improved regularization algorithm under marginality principle. We also establish the asymptotic properties of the penalized estimator and provide the corresponding excess risk. Our Monte Carlo simulations illustrate the proposed model and method, which are then applied to the analysis of Parkinson’s disease rating scores and further verify the effectiveness of a novel Parkinson’s disease (PD) treatment. Full article
(This article belongs to the Section D1: Probability and Statistics)
►▼ Show Figures

Figure 1

32 pages, 876 KiB  
Article
Physics-Informed Neural Networks and Fourier Methods for the Generalized Korteweg–de Vries Equation
by Rubén Darío Ortiz Ortiz, Ana Magnolia Marín Ramírez and Miguel Ángel Ortiz Marín
Mathematics 2025, 13(9), 1521; https://doi.org/10.3390/math13091521 - 5 May 2025
Viewed by 63
Abstract
We conducted a comprehensive comparative study of numerical solvers for the generalized Korteweg–de Vries (gKdV) equation, focusing on classical Fourier-based Crank–Nicolson methods and physics-informed neural networks (PINNs). Our work benchmarks these approaches across nonlinear regimes—including the cubic case (ν=3)—and [...] Read more.
We conducted a comprehensive comparative study of numerical solvers for the generalized Korteweg–de Vries (gKdV) equation, focusing on classical Fourier-based Crank–Nicolson methods and physics-informed neural networks (PINNs). Our work benchmarks these approaches across nonlinear regimes—including the cubic case (ν=3)—and diverse initial conditions such as solitons, smooth pulses, discontinuities, and noisy profiles. In addition to pure PINN and spectral models, we propose a novel hybrid PINN–spectral method incorporating a regularization term based on Fourier reference solutions, leading to improved accuracy and stability. Numerical experiments show that while spectral methods achieve superior efficiency in structured domains, PINNs provide flexible, mesh-free alternatives for data-driven and irregular setups. The hybrid model achieves lower relative L2 error and better captures soliton interactions. Our results demonstrate the complementary strengths of spectral and machine learning methods for nonlinear dispersive PDEs. Full article
(This article belongs to the Special Issue Asymptotic Analysis and Applications)
►▼ Show Figures

Figure 1

25 pages, 1867 KiB  
Article
Nonlinear Mathematical Modeling and Robust Control of UAV Formation Under Parametric Variations and External Disturbances
by Claudia Verónica Vera Vaca, Stefano Di Gennaro, Claudia Carolina Vaca García and Cuauhtémoc Acosta Lúa
Mathematics 2025, 13(9), 1520; https://doi.org/10.3390/math13091520 - 5 May 2025
Viewed by 70
Abstract
This paper introduces a robust formation control strategy for Unmanned Aerial Vehicles (UAVs) designed to maintain coordinated trajectories and relative positioning in three-dimensional space. The proposed methodology addresses the challenges of parametric uncertainties and external disturbances by employing a backstepping-based framework with integrated [...] Read more.
This paper introduces a robust formation control strategy for Unmanned Aerial Vehicles (UAVs) designed to maintain coordinated trajectories and relative positioning in three-dimensional space. The proposed methodology addresses the challenges of parametric uncertainties and external disturbances by employing a backstepping-based framework with integrated proportional-integral virtual controls. The control strategy stabilizes tracking errors in the x, y, and z axes, ensuring that the UAVs maintain a cohesive formation even in the presence of dynamic model variations and environmental perturbations. The approach combines dynamic models of UAV motion, incorporating translational and rotational behaviors, with a decomposition of relative distances in the leader’s local reference frame to ensure precise formation control. This framework enhances stability, trajectory tracking, and disturbance rejection. Validation through MATLAB-Simulink simulations demonstrates the effectiveness of the proposed strategy, showcasing its ability to maintain formation and trajectory adherence under diverse operating conditions. The results emphasize the robustness and flexibility of the control approach, making it suitable for demanding applications requiring precise multi-UAV coordination. Full article
(This article belongs to the Special Issue Advances in Nonlinear Control Theory Applied to Dynamic Systems)
►▼ Show Figures

Figure 1

15 pages, 983 KiB  
Article
Task-Oriented Local Feature Rectification Network for Few-Shot Image Classification
by Ping Li and Xiang Zhu
Mathematics 2025, 13(9), 1519; https://doi.org/10.3390/math13091519 - 5 May 2025
Viewed by 113
Abstract
Few-shot image classification aims to classify unlabeled samples when only a small number of labeled samples are available for each class. Recently, local feature-based few-shot learning methods have made significant progress. However, existing methods often treat all local descriptors equally, without considering the [...] Read more.
Few-shot image classification aims to classify unlabeled samples when only a small number of labeled samples are available for each class. Recently, local feature-based few-shot learning methods have made significant progress. However, existing methods often treat all local descriptors equally, without considering the importance of each local descriptor in different tasks. Therefore, the few-shot learning model is easily disturbed by class-irrelevant features, which results in a decrease in accuracy. To address this issue, we propose a task-oriented local feature rectification network (TLFRNet) with two feature rectification modules (support rectification module and query rectification module). The former module uses the relationship between each local descriptor and prototypes within the support set to rectify the support features. The latter module uses a CNN to rectify the similarity tensors between the query and support local features and then models the importance of the query local features. Through these two modules, our model can effectively reduce the intra-class variation of class-relevant features, thus obtaining more accurate image-to-class similarity for classification. Extensive experiments on five datasets show that TLFRNet achieves more superior classification performance than the related methods. Full article
(This article belongs to the Topic Soft Computing and Machine Learning)
►▼ Show Figures

Figure 1

27 pages, 1276 KiB  
Article
Transient Post-Buckling of Microfluid-Conveying FG-CNTs Cylindrical Microshells Embedded in Kerr Foundation and Exposed to a 2D Magnetic Field
by Mohammed Sobhy
Mathematics 2025, 13(9), 1518; https://doi.org/10.3390/math13091518 - 5 May 2025
Viewed by 72
Abstract
Dynamic post-buckling behavior of microscale cylindrical shells reinforced with functionally graded carbon nanotubes (FG-CNTs) and conveying microfluid is discussed for the first time. The microshell is embedded in a Kerr foundation and subjected to an axial compressive load and a two-dimensional magnetic field [...] Read more.
Dynamic post-buckling behavior of microscale cylindrical shells reinforced with functionally graded carbon nanotubes (FG-CNTs) and conveying microfluid is discussed for the first time. The microshell is embedded in a Kerr foundation and subjected to an axial compressive load and a two-dimensional magnetic field effect. CNTs dispersion across the shell thickness follows a power law, with five distribution types developed. The modified couple stress theory is applied to incorporate the small-size effect using a single material parameter. Furthermore, the Knudsen number is used to address the small-size effect on the microfluid. The external force between the magnetic fluid and microshell is modeled by applying the Navier–Stokes equation depending on the fluid velocity. Nonlinear motion equations of the present model are derived using Hamilton’s principle, containing the Lorentz magnetic force. According to the Galerkin method, the equations of motion are transformed into an algebraic system to be solved, determining the post-buckling paths. Numerical results indicate that the presence of the magnetic field, CNT reinforcement, and fluid flow improves the load-bearing performance of the cylindrical microshells. Also, many new parametric effects on the post-buckling curves of the FG-CNT microshells have been discovered, including the shell geometry, magnetic field direction, length scale parameter, Knudsen number, and CNT distribution types. Full article
►▼ Show Figures

Figure 1

32 pages, 5779 KiB  
Article
Modeling Rural Labor Responses to Digital Finance: A Hybrid IGSA-Random Forest Approach
by Zhiru Lin and Yishuai Tian
Mathematics 2025, 13(9), 1517; https://doi.org/10.3390/math13091517 - 4 May 2025
Viewed by 290
Abstract
The application of digital inclusive finance in various industries, particularly in rural areas, is gaining significant attention. The traditional agricultural sector, which focuses on rural labor economics (RLE), is more sensitive to financial innovations due to geographical and other constraints. This paper investigates [...] Read more.
The application of digital inclusive finance in various industries, particularly in rural areas, is gaining significant attention. The traditional agricultural sector, which focuses on rural labor economics (RLE), is more sensitive to financial innovations due to geographical and other constraints. This paper investigates how digital inclusive finance affects RLE by integrating the Improved Gravitational Search Algorithm Random Forest (IGSA-RF) with the Gini coefficient, Out-of-Bag (OOB) coefficient, and the Gini-OOB coupling coefficient. Focusing on Jiangsu Province, China, this study uses rural labor economic indicators to examine the underlying influence mechanisms of digital finance on labor dynamics in rural regions. The findings suggest that (1) digital inclusive finance has a long-term positive impact on consumption, gross regional product, and the average wage index of rural workers; (2) there is a growing trend in agricultural machinery power over time. However, the study found that gender, age, and the development of labor-intensive industries did not show significant improvement. The study provides a data-driven framework for understanding and enhancing rural labor development through digital financial innovation. Full article
(This article belongs to the Special Issue Mathematical Modelling in Financial Economics)
►▼ Show Figures

Figure 1

23 pages, 3914 KiB  
Article
Tensor-Based Uncoupled and Incomplete Multi-View Clustering
by Yapeng Liu, Wei Guo, Weiyu Li, Jingfeng Su, Qianlong Zhou and Shanshan Yu
Mathematics 2025, 13(9), 1516; https://doi.org/10.3390/math13091516 - 4 May 2025
Viewed by 86
Abstract
Multi-view clustering demonstrates strong performance in various real-world applications. However, real-world data often contain incomplete and uncoupled views. Missing views can lead to the loss of latent information, and uncoupled views create obstacles for cross-view learning. Existing methods rarely consider incomplete and uncoupled [...] Read more.
Multi-view clustering demonstrates strong performance in various real-world applications. However, real-world data often contain incomplete and uncoupled views. Missing views can lead to the loss of latent information, and uncoupled views create obstacles for cross-view learning. Existing methods rarely consider incomplete and uncoupled multi-view data simultaneously. To address these problems, a novel method called Tensor-based Uncoupled and Incomplete Multi-view Clustering (TUIMC) is proposed to effectively handle incomplete and uncoupled data. Specifically, the proposed method recovers missing samples in a low-dimensional feature space. Subsequently, the self-representation matrices are paired with the optimal views through permutation matrices. The coupled self-representation matrices are integrated into a third-order tensor to explore high-order information of multi-view data. An efficient algorithm is designed to solve the proposed model. Experimental results on five widely used benchmark datasets show that the proposed method exhibits superior clustering performance on incomplete and uncoupled multi-view data. Full article
►▼ Show Figures

Figure 1

19 pages, 5504 KiB  
Article
Progressive Domain Decomposition for Efficient Training of Physics-Informed Neural Network
by Dawei Luo, Soo-Ho Jo and Taejin Kim
Mathematics 2025, 13(9), 1515; https://doi.org/10.3390/math13091515 - 4 May 2025
Viewed by 183
Abstract
This study proposes a strategy for decomposing the computational domain to solve differential equations using physics-informed neural networks (PINNs) and progressively saving the trained model in each subdomain. The proposed progressive domain decomposition (PDD) method segments the domain based on the dynamics of [...] Read more.
This study proposes a strategy for decomposing the computational domain to solve differential equations using physics-informed neural networks (PINNs) and progressively saving the trained model in each subdomain. The proposed progressive domain decomposition (PDD) method segments the domain based on the dynamics of residual loss, thereby indicating the complexity of different sections within the entire domain. By analyzing residual loss pointwise and aggregating it over specific intervals, we identify critical regions requiring focused attention. This strategic segmentation allows for the application of tailored neural networks in identified subdomains, each characterized by varying levels of complexity. Additionally, the proposed method trains and saves the model progressively based on performance metrics, thereby conserving computational resources in sections where satisfactory results are achieved during the training process. The effectiveness of PDD is demonstrated through its application to complex PDEs, where it significantly enhances accuracy and conserves computational power by strategically simplifying the computational tasks into manageable segments. Full article
(This article belongs to the Special Issue Advanced Modeling and Design of Vibration and Wave Systems)
►▼ Show Figures

Figure 1

19 pages, 4281 KiB  
Article
Volatility Spillover Between China’s Carbon Market and Traditional Manufacturing
by Jining Wang, Dian Sheng and Lei Wang
Mathematics 2025, 13(9), 1514; https://doi.org/10.3390/math13091514 - 4 May 2025
Viewed by 189
Abstract
This study constructed a DGC-t-MSV model by integrating dynamic correlation and Granger causality into the MSV framework. Using daily closing price data from 4 January 2022 to 21 November 2024, it empirically analyzed volatility spillover effects between China’s carbon market and traditional manufacturing [...] Read more.
This study constructed a DGC-t-MSV model by integrating dynamic correlation and Granger causality into the MSV framework. Using daily closing price data from 4 January 2022 to 21 November 2024, it empirically analyzed volatility spillover effects between China’s carbon market and traditional manufacturing from an industrial heterogeneity perspective. The findings are as follows: (1) The carbon market exhibits significant unidirectional volatility spillover effects on carbon-intensive industries, such as steel, chemicals, shipbuilding, and automobile manufacturing, with the carbon market acting as the spillover source. (2) Bidirectional volatility spillover effects exist between the carbon market and industries such as forest products, textiles, construction engineering, and machinery manufacturing, with the carbon market predominantly acting as a recipient. (3) The carbon market exhibits general dynamic correlations with traditional manufacturing industries, where the correlation strength is positively associated with industry-level carbon emissions. Notably, the correlations with the steel, chemicals, machinery manufacturing, construction engineering, and automobile manufacturing industries are significant, whereas those with the textile industry and the forest products industry are relatively weaker. Furthermore, the carbon market demonstrates substantially higher volatility than traditional manufacturing industries. This study innovatively explored volatility spillover effects between China’s carbon market and traditional manufacturing from an industrial heterogeneity perspective, providing policy implications for their coordinated development. Full article
(This article belongs to the Special Issue Mathematics and Applications)
►▼ Show Figures

Figure 1

37 pages, 927 KiB  
Article
CISMN: A Chaos-Integrated Synaptic-Memory Network with Multi-Compartment Chaotic Dynamics for Robust Nonlinear Regression
by Yaser Shahbazi, Mohsen Mokhtari Kashavar, Abbas Ghaffari, Mohammad Fotouhi and Siamak Pedrammehr
Mathematics 2025, 13(9), 1513; https://doi.org/10.3390/math13091513 - 4 May 2025
Viewed by 138
Abstract
Modeling complex, non-stationary dynamics remains challenging for deterministic neural networks. We present the Chaos-Integrated Synaptic-Memory Network (CISMN), which embeds controlled chaos across four modules—Chaotic Memory Cells, Chaotic Plasticity Layers, Chaotic Synapse Layers, and a Chaotic Attention Mechanism—supplemented by a logistic-map learning-rate schedule. Rigorous [...] Read more.
Modeling complex, non-stationary dynamics remains challenging for deterministic neural networks. We present the Chaos-Integrated Synaptic-Memory Network (CISMN), which embeds controlled chaos across four modules—Chaotic Memory Cells, Chaotic Plasticity Layers, Chaotic Synapse Layers, and a Chaotic Attention Mechanism—supplemented by a logistic-map learning-rate schedule. Rigorous stability analyses (Lyapunov exponents, boundedness proofs) and gradient-preservation guarantees underpin our design. In experiments, CISMN-1 on a synthetic acoustical regression dataset (541 samples, 22 features) achieved R2 = 0.791 and RMSE = 0.059, outpacing physics-informed and attention-augmented baselines. CISMN-4 on the PMLB sonar benchmark (208 samples, 60 bands) attained R2 = 0.424 and RMSE = 0.380, surpassing LSTM, memristive, and reservoir models. Across seven standard regression tasks with 5-fold cross-validation, CISMN led on diabetes (R2 = 0.483 ± 0.073) and excelled in high-dimensional, low-sample regimes. Ablations reveal a scalability–efficiency trade-off: lightweight variants train in < 10 s with > 95% peak accuracy, while deeper configurations yield marginal gains. CISMN sustains gradient norms (~2 300) versus LSTM collapse (<3), and fixed-seed protocols ensure < 1.2% MAE variation. Interpretability remains challenging (feature-attribution entropy ≈ 2.58 bits), motivating future hybrid explanation methods. CISMN recasts chaos as a computational asset for robust, generalizable modeling across scientific, financial, and engineering domains. Full article
(This article belongs to the Special Issue Advances in Machine Learning and Graph Neural Networks)
16 pages, 581 KiB  
Article
Semi-Global Polynomial Synchronization of High-Order Multiple Proportional-Delay BAM Neural Networks
by Er-yong Cong, Xian Zhang and Li Zhu
Mathematics 2025, 13(9), 1512; https://doi.org/10.3390/math13091512 - 4 May 2025
Viewed by 189
Abstract
This paper addresses the semi-global polynomial synchronization (SGPS) problem for a class of high-order bidirectional associative memory neural networks (HOBAMNNs) with multiple proportional delays. The time-delay-dependent semi-global polynomial stability criterion for error systems was established via a direct approach. The derived stability conditions [...] Read more.
This paper addresses the semi-global polynomial synchronization (SGPS) problem for a class of high-order bidirectional associative memory neural networks (HOBAMNNs) with multiple proportional delays. The time-delay-dependent semi-global polynomial stability criterion for error systems was established via a direct approach. The derived stability conditions are formulated as several simple inequalities that are readily solvable, facilitating direct verification using standard computational tools (e.g., YALMIP). Notably, this method can be applied to many system models with proportional delays after minor modifications. Finally, a numerical example is provided to validate the effectiveness of the theoretical results. Full article
(This article belongs to the Special Issue Advances in Study of Time-Delay Systems and Their Applications, 2nd Edition)
►▼ Show Figures

Figure 1

14 pages, 351 KiB  
Article
Efficient Numerical Methods for Reaction–Diffusion Problems Governed by Singularly Perturbed Fredholm Integro-Differential Equations
by Sekar Elango, Lolugu Govindarao, Muath Awadalla and Hajer Zaway
Mathematics 2025, 13(9), 1511; https://doi.org/10.3390/math13091511 - 4 May 2025
Viewed by 117
Abstract
A set of singularly perturbed systems comprising Fredholm integro-differential equations associated with reaction–diffusion problems is considered. To approximate solutions to these systems, a second-order scheme for the derivatives and the trapezoidal rule for the integral terms are utilized. The discretization is performed on [...] Read more.
A set of singularly perturbed systems comprising Fredholm integro-differential equations associated with reaction–diffusion problems is considered. To approximate solutions to these systems, a second-order scheme for the derivatives and the trapezoidal rule for the integral terms are utilized. The discretization is performed on non-standard grids known as Shishkin-type meshes. The numerical method demonstrates a second-order rate of convergence with respect to small parameters in the equations, and error estimates are derived in the discrete maximum norm. Numerical experiments are conducted to verify the theoretical results. Full article
►▼ Show Figures

Figure 1

22 pages, 1054 KiB  
Article
Partially Symmetric Regularized Two-Step Inertial Alternating Direction Method of Multipliers for Non-Convex Split Feasibility Problems
by Can Yang and Yazheng Dang
Mathematics 2025, 13(9), 1510; https://doi.org/10.3390/math13091510 - 4 May 2025
Viewed by 106
Abstract
This paper presents a partially symmetric regularized two-step inertial alternating direction method of multipliers for solving non-convex split feasibility problems (SFP), which adds a two-step inertial effect to each subproblem and includes an intermediate update term for multipliers during the iteration process. Under [...] Read more.
This paper presents a partially symmetric regularized two-step inertial alternating direction method of multipliers for solving non-convex split feasibility problems (SFP), which adds a two-step inertial effect to each subproblem and includes an intermediate update term for multipliers during the iteration process. Under suitable assumptions, the global convergence is demonstrated. Additionally, with the help of the Kurdyka−Łojasiewicz (KL) property, which quantifies the behavior of a function near its critical points, the strong convergence of the proposed algorithm is guaranteed. Numerical experiments are performed to demonstrate the efficacy. Full article
►▼ Show Figures

Figure 1

21 pages, 9588 KiB  
Article
Optimal Design Considering AC Copper Loss of Traction Motor Applied HSFF Coil for Improving Electric Bus Fuel Economy
by Kyoung-Soo Cha, Young-Hoon Jung, Soo-Hwan Park and Min-Ro Park
Mathematics 2025, 13(9), 1509; https://doi.org/10.3390/math13091509 - 3 May 2025
Viewed by 161
Abstract
Improving the fuel economy of electric buses requires traction motors that provide not only high-power density but also high efficiency under diverse driving conditions. While high slot fill factor (HSFF) coils such as the maximum slot occupation (MSO) coil improve motor torque and [...] Read more.
Improving the fuel economy of electric buses requires traction motors that provide not only high-power density but also high efficiency under diverse driving conditions. While high slot fill factor (HSFF) coils such as the maximum slot occupation (MSO) coil improve motor torque and power density, they inevitably increase AC copper losses due to elevated AC resistance, especially at high speeds. Unlike conventional motor optimization studies that mainly focus on efficiency at specific operating points, this paper proposes a drive-cycle-aware design optimization method that minimizes AC copper loss to enhance real-world fuel economy. By combining 2D finite element analysis (FEA) with vehicle-level simulations under three representative driving cycles (Manhattan, HWFET, HDUDDS), an optimal motor design was derived. The optimized motor achieved improvements in fuel economy by 0.20%, 0.86%, and 0.36%, respectively, compared to the initial design. Experimental validation through prototype fabrication confirmed the effectiveness of the proposed method. These results demonstrate that the proposed design approach can contribute to improving energy efficiency and reducing operational costs in electric bus applications. Full article
(This article belongs to the Special Issue Applied Mathematics to Mechanisms and Machines II)
►▼ Show Figures

Figure 1

17 pages, 1144 KiB  
Article
Efficient Numerical Quadrature for Highly Oscillatory Integrals with Bessel Function Kernels
by Guo He and Yuying Liu
Mathematics 2025, 13(9), 1508; https://doi.org/10.3390/math13091508 - 3 May 2025
Viewed by 104
Abstract
In this paper, we investigate efficient numerical methods for highly oscillatory integrals with Bessel function kernels over finite and infinite domains. Initially, we decompose the two types of integrals into the sum of two integrals. For one of these integrals, we reformulate the [...] Read more.
In this paper, we investigate efficient numerical methods for highly oscillatory integrals with Bessel function kernels over finite and infinite domains. Initially, we decompose the two types of integrals into the sum of two integrals. For one of these integrals, we reformulate the Bessel function Jν(z) as a linear combination of the modified Bessel function of the second kind Kν(z), subsequently transforming it into a line integral over an infinite interval on the complex plane. This transformation allows for efficient approximation using the Cauchy residue theorem and appropriate Gaussian quadrature rules. For the other integral, we achieve efficient computation by integrating special functions with Gaussian quadrature rules. Furthermore, we conduct an error analysis of the proposed methods and validate their effectiveness through numerical experiments. The proposed methods are applicable for any real number ν and require only the first ⌊ν⌋ derivatives of f at 0, rendering them more efficient than existing methods that typically necessitate higher-order derivatives. Full article
►▼ Show Figures

Figure 1

27 pages, 7355 KiB  
Article
Research on Dynamic Decision-Making of Shared Supply Chain Considering Multi-Agent Altruistic Preferences
by Ran Gu, Yifan Zhao, Enhui Ding and Shigui Ma
Mathematics 2025, 13(9), 1507; https://doi.org/10.3390/math13091507 - 3 May 2025
Viewed by 148
Abstract
Shared supply chains (SSCs) represent a critical practice in the field of the sharing economy. With the aid of digital technologies, SSCs improve resource utilization through efficiently re-allocating and sharing. This paper develops a three-tier SSC model comprising a supplier, a retailer, and [...] Read more.
Shared supply chains (SSCs) represent a critical practice in the field of the sharing economy. With the aid of digital technologies, SSCs improve resource utilization through efficiently re-allocating and sharing. This paper develops a three-tier SSC model comprising a supplier, a retailer, and a sharing platform. The model is based on a Stackelberg dynamic framework and incorporates both resource sharing and altruistic behaviors. Our findings reveal that different altruistic modes significantly alter members’ decision logics: supplier altruism is manifested by lower supply prices and enhanced supply efforts; retailer altruism improves system supply efficiency through increased supply efforts; and the sharing platform, through resource integration and service optimization, comprehensively elevates overall SSC operations. Furthermore, numerical experimental analysis indicated that as altruistic parameters increased, overall system performance improved significantly. Notably, the marginal contribution of platform altruism surpassed that of both the supplier and the retailer, underscoring its pivotal role as a central hub in SSC systems. In addition, joint altruism can achieve a Pareto improvement for both individual members and overall system utility. This study provides an important theoretical basis for designing multi-agent collaborative mechanisms in SSCs. Full article
(This article belongs to the Special Issue Mathematical Modelling and Optimization of Service Supply Chain, 2nd Edition)
►▼ Show Figures

Figure 1

26 pages, 3782 KiB  
Article
Semiparametric Estimation and Application of Realized GARCH Model with Time-Varying Leverage Effect
by Jinguan Lin, Yizhi Mao, Hongxia Hao and Guangying Liu
Mathematics 2025, 13(9), 1506; https://doi.org/10.3390/math13091506 - 2 May 2025
Viewed by 182
Abstract
To describe the stylized features of volatility comprehensively, this paper embeds the time-varying leverage effect of volatility into the Realized Generalized AutoRegressive Conditional Heteroskedasticity (RG) model and proposes a new volatility model with a time-varying leverage effect. The Quasi-Maximum Likelihood-Kernel (QML-K) method is [...] Read more.
To describe the stylized features of volatility comprehensively, this paper embeds the time-varying leverage effect of volatility into the Realized Generalized AutoRegressive Conditional Heteroskedasticity (RG) model and proposes a new volatility model with a time-varying leverage effect. The Quasi-Maximum Likelihood-Kernel (QML-K) method is proposed to approximate the density function of returns and to estimate the parameters in the new model. Under some mild regularity conditions, the asymptotic properties of the resulting estimators are achieved. Simulation studies demonstrate that the proposed model yields better performances than traditional RG models under different situations. Finally, the empirical analysis shows better finite sample performance of the estimation method and the new model on real data compared with existing methods. Full article
(This article belongs to the Section E5: Financial Mathematics)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-174
Previous Issue
Back to TopTop