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Mathematics, Volume 13, Issue 21 (November-1 2025) – 43 articles

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16 pages, 505 KB  
Article
Estimating the Number of Junta Variables for Optimizing Boolean Functions in Quantum Memories
by Abdulaziz Alotaibi, Samar AbdelAzim, Sattam Saleem Alharbi and Mohamed Darwish
Mathematics 2025, 13(21), 3400; https://doi.org/10.3390/math13213400 (registering DOI) - 25 Oct 2025
Abstract
Optimizing Boolean function components to have the minimum number of inputs in order to reduce the memory space required during these functions in computing devices is a significant demand. This paper proposes a quantum computation approach based on the degree-of-entanglement quantum computation model [...] Read more.
Optimizing Boolean function components to have the minimum number of inputs in order to reduce the memory space required during these functions in computing devices is a significant demand. This paper proposes a quantum computation approach based on the degree-of-entanglement quantum computation model to estimate the number of junta variables of an unknown Boolean function presented through an oracle. The time complexity of the developed quantum approach is independent of the number of inputs and depends on an allowable assigned error ϵ. Thus, the time complexity of the developed algorithm is O(ϵ−2), compared to O(2n+1) in the traditional approach. Also, the memory space of the developed approach is linear, O(2n+4), in terms of the number of inputs compared to the exponential memory space O(2n+1) using the traditional approach. Therefore, the developed quantum approach has exponential supremacy in comparison to the traditional approach. The developed approach was implemented practically using both the Qiskit simulator and the IBM real quantum computer. The obtained results expose high statistical fidelities between the empirical and theoretical results. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
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9 pages, 227 KB  
Article
Green’s Functions for Neumann Boundary Conditions
by Jerrold Franklin
Mathematics 2025, 13(21), 3399; https://doi.org/10.3390/math13213399 (registering DOI) - 25 Oct 2025
Abstract
Green’s functions for Neumann boundary conditions have been considered in Math, Physics, and Electromagnetism textbooks, but often with mistakes of omission and commission. Special constraints and other properties required for Neumann boundary conditions have generally not been noticed or treated correctly. In this [...] Read more.
Green’s functions for Neumann boundary conditions have been considered in Math, Physics, and Electromagnetism textbooks, but often with mistakes of omission and commission. Special constraints and other properties required for Neumann boundary conditions have generally not been noticed or treated correctly. In this paper, we derive appropriate Neumann Green’s functions with these properties properly incorporated. Full article
16 pages, 14135 KB  
Article
Underwater Image Enhancement with a Hybrid U-Net-Transformer and Recurrent Multi-Scale Modulation
by Zaiming Geng, Jiabin Huang, Xiaotian Wang, Yu Zhang, Xinnan Fan and Pengfei Shi
Mathematics 2025, 13(21), 3398; https://doi.org/10.3390/math13213398 (registering DOI) - 25 Oct 2025
Abstract
The quality of underwater imagery is inherently degraded by light absorption and scattering, a challenge that severely limits its application in critical domains such as marine robotics and archeology. While existing enhancement methods, including recent hybrid models, attempt to address this, they often [...] Read more.
The quality of underwater imagery is inherently degraded by light absorption and scattering, a challenge that severely limits its application in critical domains such as marine robotics and archeology. While existing enhancement methods, including recent hybrid models, attempt to address this, they often struggle to restore fine-grained details without introducing visual artifacts. To overcome this limitation, this work introduces a novel hybrid U-Net-Transformer (UTR) architecture that synergizes local feature extraction with global context modeling. The core innovation is a Recurrent Multi-Scale Feature Modulation (R-MSFM) mechanism, which, unlike prior recurrent refinement techniques, employs a gated modulation strategy across multiple feature scales within the decoder to iteratively refine textural and structural details with high fidelity. This approach effectively preserves spatial information during upsampling. Extensive experiments demonstrate the superiority of the proposed method. On the EUVP dataset, UTR achieves a PSNR of 28.347 dB, a significant gain of +3.947 dB over the state-of-the-art UWFormer. Moreover, it attains a top-ranking UIQM score of 3.059 on the UIEB dataset, underscoring its robustness. The results confirm that UTR provides a computationally efficient and highly effective solution for underwater image enhancement. Full article
(This article belongs to the Special Issue Artificial Intelligence, Algorithms, and Databases: Innovations and Cross-Disciplinary Impact)
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40 pages, 2911 KB  
Article
A Vehicle Routing Problem Based on a Long-Distance Transportation Network with an Exact Optimization Algorithm
by Toygar Emre and Rızvan Erol
Mathematics 2025, 13(21), 3397; https://doi.org/10.3390/math13213397 (registering DOI) - 24 Oct 2025
Abstract
In vehicle routing problems, long-distance transportation poses a significant challenge to the optimization of transportation costs while adhering to regulations. This study investigates a special type of logistics problem that focuses on liquid transportation systems involving full truckload delivery and the rest–break–drive periods [...] Read more.
In vehicle routing problems, long-distance transportation poses a significant challenge to the optimization of transportation costs while adhering to regulations. This study investigates a special type of logistics problem that focuses on liquid transportation systems involving full truckload delivery and the rest–break–drive periods of truck drivers over long distances according to the regulations of the United States. Based on an exact solution algorithm, this work combines a long-distance full truckload fluid transportation problem with the concept of truck driver schedules for the first time. The goal is to optimize transportation expenses while managing challenges related to the rest–break–drive periods of truck drivers, time windows, trailer varieties, customer segments, food and non-food products, a diverse fleet, starting locations, and the diverse tasks of vehicles. In order to reach optimality, a construction heuristic and the column generation method were employed, supplemented by several acceleration strategies. Performance analysis, carried out with artificial input sets mirroring real-life scenarios, indicates that low optimality gaps can be obtained in an appropriate amount of time for large-scale long-haul liquid transportation. Full article
(This article belongs to the Special Issue Optimization and Mathematical Modelling in Transport and Logistics Network)
25 pages, 1288 KB  
Article
An Analysis of Implied Volatility, Sensitivity, and Calibration of the Kennedy Model
by Dalma Tóth-Lakits, Miklós Arató and András Ványolos
Mathematics 2025, 13(21), 3396; https://doi.org/10.3390/math13213396 (registering DOI) - 24 Oct 2025
Abstract
The Kennedy model provides a flexible and mathematically consistent framework for modeling the term structure of interest rates, leveraging Gaussian random fields to capture the dynamics of forward rates. Building upon our earlier work, where we developed both theoretical results—including novel proofs of [...] Read more.
The Kennedy model provides a flexible and mathematically consistent framework for modeling the term structure of interest rates, leveraging Gaussian random fields to capture the dynamics of forward rates. Building upon our earlier work, where we developed both theoretical results—including novel proofs of the martingale property, connections between the Kennedy and HJM frameworks, and parameter estimation theory—and practical calibration methods, using maximum likelihood, Radon–Nikodym derivatives, and numerical optimization (stochastic gradient descent) on simulated and real par swap rate data, this study extends the analysis in several directions. We derive detailed formulas for the volatilities implied by the Kennedy model and investigate their asymptotic properties. A comprehensive sensitivity analysis is conducted to evaluate the impact of key parameters on derivative prices. We implement an industry-standard Monte Carlo method, tailored to the conditional distribution of the Kennedy field, to efficiently generate scenarios consistent with observed initial forward curves. Furthermore, we present closed-form pricing formulas for various interest rate derivatives, including zero-coupon bonds, caplets, floorlets, swaplets, and the par swap rate. A key advantage of these results is that the formulas are expressed explicitly in terms of the initial forward curve and the original parameters of the Kennedy model, which ensures both analytical tractability and consistency with market-observed data. These closed-form expressions can be directly utilized in calibration procedures, substantially accelerating multidimensional nonlinear optimization algorithms. Moreover, given an observed initial forward curve, the model provides significantly more accurate pricing formulas, enhancing both theoretical precision and practical applicability. Finally, we calibrate the Kennedy model to market-observed caplet prices. The findings provide valuable insights into the practical applicability and robustness of the Kennedy model in real-world financial markets. Full article
(This article belongs to the Special Issue Modern Trends in Mathematics, Probability and Statistics for Finance)
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30 pages, 1382 KB  
Article
Asymptotic Analysis of the Bias–Variance Trade-Off in Subsampling Metropolis–Hastings
by Shuang Liu
Mathematics 2025, 13(21), 3395; https://doi.org/10.3390/math13213395 (registering DOI) - 24 Oct 2025
Abstract
Markov chain Monte Carlo (MCMC) methods are fundamental to Bayesian inference but are often computationally prohibitive for large datasets, as the full likelihood must be evaluated at each iteration. Subsampling-based approximate Metropolis–Hastings (MH) algorithms offer a popular alternative, trading a manageable bias for [...] Read more.
Markov chain Monte Carlo (MCMC) methods are fundamental to Bayesian inference but are often computationally prohibitive for large datasets, as the full likelihood must be evaluated at each iteration. Subsampling-based approximate Metropolis–Hastings (MH) algorithms offer a popular alternative, trading a manageable bias for a significant reduction in per-iteration cost. While this bias–variance trade-off is empirically understood, a formal theoretical framework for its optimization has been lacking. Our work establishes such a framework by bounding the mean squared error (MSE) as a function of the subsample size (m), the data size (n), and the number of epochs (E). This analysis reveals two optimal asymptotic scaling laws: the optimal subsample size is m★=O(E1/2), leading to a minimal MSE that scales as MSE★=O(E−1/2). Furthermore, leveraging the large-sample asymptotic properties of the posterior, we show that when augmented with a control variate, the approximate MH algorithm can be asymptotically more efficient than the standard MH method under ideal conditions. Experimentally, we first validate the two optimal asymptotic scaling laws. We then use Bayesian logistic regression and Softmax classification models to highlight a key difference in convergence behavior: the exact algorithm starts with a high MSE that gradually decreases as the number of epochs increases. In contrast, the approximate algorithm with a practical control variate maintains a consistently low MSE that is largely insensitive to the number of epochs. Full article
20 pages, 2260 KB  
Article
Null Space Properties of Neural Networks with Applications to Image Steganography
by Xiang Li and Kevin M. Short
Mathematics 2025, 13(21), 3394; https://doi.org/10.3390/math13213394 (registering DOI) - 24 Oct 2025
Abstract
This paper advances beyond adversarial neural network methods by considering whether the underlying mathematics of neural networks contains inherent properties that can be exploited to fool neural networks. In broad terms, this paper will consider a neural network to be composed of a [...] Read more.
This paper advances beyond adversarial neural network methods by considering whether the underlying mathematics of neural networks contains inherent properties that can be exploited to fool neural networks. In broad terms, this paper will consider a neural network to be composed of a series of linear transformations between layers of the network, interspersed with nonlinear stages that serve to compress outliers. The input layer of the network is typically extremely high-dimensional, yet the final classification is in a space of a much lower dimension. This dimensional reduction leads to the existence of a null space, and this paper will explore how that can be exploited. Specifically, this paper explores the null space properties of neural networks by extending the null space definition from linear to nonlinear maps and discussing the presence of a null space in neural networks. The null space of a neural network characterizes the component of input data that makes no contribution to the final prediction so that we can exploit it to trick the neural network. One application described here leads to a method of image steganography. Through experiments on image data sets such as MNIST, it has been shown that the null space components can be used to force the neural network to choose a selected hidden image class, even though the overall image can be made to look like a completely different image. The paper concludes with comparisons between what a human viewer would see and the part of the image that the neural network is actually using to make predictions, hence showing that what the neural network “sees” is completely different than what we would expect. Full article
27 pages, 344 KB  
Article
𝒜-Joint Numerical Radius Bounds for Operator Pairs in Semi-Hilbert Spaces with Applications
by Amani Baazeem, Silvestru Sever Dragomir and Kais Feki
Mathematics 2025, 13(21), 3393; https://doi.org/10.3390/math13213393 (registering DOI) - 24 Oct 2025
Abstract
Consider a complex Hilbert space X,⟨·,·⟩ equipped with a positive (semidefinite) bounded linear operator A on X. The A-joint numerical radius for two A-bounded operators T and S is defined as [...] Read more.
Consider a complex Hilbert space X,⟨·,·⟩ equipped with a positive (semidefinite) bounded linear operator A on X. The A-joint numerical radius for two A-bounded operators T and S is defined as ωA,e(T,S)=sup∥x∥A=1⟨Tx,x⟩A2+⟨Sx,x⟩A2. Among other results, in this study we demonstrate that ωe,A2T,S≤21−1rmaxTA2r,SA2r+ωArS♯AT1r for r≥1 and that ωe,A2T,S≥12ωAT2+S2+12maxωAS+T,ωAS−TωAS−ωAT. Additionally, we provide several inequalities related to the A-numerical radius and A-seminorm. Full article
(This article belongs to the Section C: Mathematical Analysis)
31 pages, 1338 KB  
Article
An Enhanced Discriminant Analysis Approach for Multi-Classification with Integrated Machine Learning-Based Missing Data Imputation
by Autcha Araveeporn and Atid Kangtunyakarn
Mathematics 2025, 13(21), 3392; https://doi.org/10.3390/math13213392 (registering DOI) - 24 Oct 2025
Abstract
This study addresses the challenge of accurate classification under missing data conditions by integrating multiple imputation strategies with discriminant analysis frameworks. The proposed approach evaluates six imputation methods (Mean, Regression, KNN, Random Forest, Bagged Trees, MissRanger) across several discriminant techniques. Simulation scenarios varied [...] Read more.
This study addresses the challenge of accurate classification under missing data conditions by integrating multiple imputation strategies with discriminant analysis frameworks. The proposed approach evaluates six imputation methods (Mean, Regression, KNN, Random Forest, Bagged Trees, MissRanger) across several discriminant techniques. Simulation scenarios varied in sample size, predictor dimensionality, and correlation structure, while the real-world application employed the Cirrhosis Prediction Dataset. The results consistently demonstrate that ensemble-based imputations, particularly regression, KNN, and MissRanger, outperform simpler approaches by preserving multivariate structure, especially in high-dimensional and highly correlated settings. MissRanger yielded the highest classification accuracy across most discriminant analysis methods in both simulated and real data, with performance gains most pronounced when combined with flexible or regularized classifiers. Regression imputation showed notable improvements under low correlation, aligning with the theoretical benefits of shrinkage-based covariance estimation. Across all methods, larger sample sizes and high correlation enhanced classification accuracy by improving parameter stability and imputation precision. Full article
(This article belongs to the Section D1: Probability and Statistics)
25 pages, 2139 KB  
Article
MIDS-GAN: Minority Intrusion Data Synthesizer GAN—An ACON Activated Conditional GAN for Minority Intrusion Detection
by Chalerm Klinkhamhom, Pongsarun Boonyopakorn and Pongpisit Wuttidittachotti
Mathematics 2025, 13(21), 3391; https://doi.org/10.3390/math13213391 (registering DOI) - 24 Oct 2025
Abstract
Intrusion Detection Systems (IDS) are vital to cybersecurity but suffer from severe class imbalance in benchmark datasets such as NSL-KDD and UNSW-NB15. Conventional oversampling methods (e.g., SMOTE, ADASYN) are efficient yet fail to preserve the latent semantics of rare attack behaviors. This study [...] Read more.
Intrusion Detection Systems (IDS) are vital to cybersecurity but suffer from severe class imbalance in benchmark datasets such as NSL-KDD and UNSW-NB15. Conventional oversampling methods (e.g., SMOTE, ADASYN) are efficient yet fail to preserve the latent semantics of rare attack behaviors. This study introduces the Minority-class Intrusion Detection Synthesizer GAN (MIDS-GAN), a divergence-minimization framework for minority data augmentation under structured feature constraints. MIDS-GAN integrates (i) correlation-based structured feature selection (SFS) to reduce redundancy, (ii) trainable ACON activations to enhance generator expressiveness, and (iii) KL-divergence-guided alignment to ensure distributional fidelity. Experiments on NSL-KDD and UNSW-NB15 demonstrate significant improvement on detection, with recall increasing from 2% to 27% for R2L and 1% to 17% for U2R in NSL-KDD, and from 18% to 44% for Worms and 69% to 75% for Shellcode in UNSW-NB15. Weighted F1-scores also improved to 78%, highlighting MIDS-GAN’s effectiveness in enhancing minority-class detection through a principled, divergence-aware approach. Full article
(This article belongs to the Special Issue Advanced Machine Learning Analysis and Application in Data Science)
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29 pages, 4643 KB  
Article
Mathematical Modeling of Light-Powered Self-Adhesion of Peeling Strips via Abrupt Transition
by Dali Ge, Shenshen Wei and Yanli Hu
Mathematics 2025, 13(21), 3390; https://doi.org/10.3390/math13213390 (registering DOI) - 24 Oct 2025
Abstract
Self-oscillating systems convert steady external stimuli into sustained motion, enabling diverse applications in robotics, energy absorption, optics, and logic. Inspired by the adhesion–detachment behavior of climbing plants, we propose a novel light-powered self-adhesion oscillator comprising an elastic strip–substrate structure and a weight suspended [...] Read more.
Self-oscillating systems convert steady external stimuli into sustained motion, enabling diverse applications in robotics, energy absorption, optics, and logic. Inspired by the adhesion–detachment behavior of climbing plants, we propose a novel light-powered self-adhesion oscillator comprising an elastic strip–substrate structure and a weight suspended by a photo-responsive liquid crystal elastomer fiber. By integrating a nonlinear beam deformation model with Dugdale’s cohesive model, we develop a nonlinear dynamic framework to describe the self-adhesion behavior of the elastic strip. Quasi-static analysis reveals two distinct operating modes: a static mode and a self-adhesion mode. Under constant light exposure, the liquid crystal elastomer fiber undergoes light-induced contraction, increasing peeling force and triggering a sudden transition from adhesion-on to adhesion-off. Upon entering the adhesion-off state, the fiber recovers its contraction, leading to a sharp return to the adhesion-on state. This cycle sustains a four-stage oscillation: gradual peeling, abrupt adhesion-off, gradual adhering, and abrupt adhesion-on. Furthermore, we identify the critical conditions for initiating self-adhesion and demonstrate effective control over the oscillation period. The system exhibits key advantages including amplitude controllable oscillation, widely tunable frequency, well-defined motion trajectories, and structural simplicity. These characteristics suggest promising potential for applications in self-healing adhesion systems, rescue devices, military engineering, and beyond. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 3rd Edition)
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16 pages, 974 KB  
Article
Dynamics of the Aggregation of Cells with Internal Oscillators
by Tilmann Glimm and Daniel Gruszka
Mathematics 2025, 13(21), 3389; https://doi.org/10.3390/math13213389 (registering DOI) - 24 Oct 2025
Abstract
We investigate two closely related Lattice Gas Cellular Automata models of the interplay of aggregation of biological cells and synchronization of intracellular oscillations (“clocks”): clock-dependent aggregation, where the adhesive forces between cells depend on their relative clock phases (akin to so-called “swarmalators”), and [...] Read more.
We investigate two closely related Lattice Gas Cellular Automata models of the interplay of aggregation of biological cells and synchronization of intracellular oscillations (“clocks”): clock-dependent aggregation, where the adhesive forces between cells depend on their relative clock phases (akin to so-called “swarmalators”), and simple adhesive aggregation, where they do not. Patterns of aggregation are similar for comparable ranges of parameters. However, while simple adhesive aggregation is quite similar to perikinetic aggregation, we show that clock-dependent aggregation differs in subtle ways. We found that it tends to inhibit coalescence of patterns and regularizes aggregate shapes, and, unintuitively, tends to enhance overall synchronization of clocks. Specifically, clock-dependent aggregation showed higher average circularity of aggregates and a larger value of Kuramoto’s r, measuring synchrony. Our results add to the growing literature on swarmalator models and give additional theoretical backing to the previously proposed idea that intracellular oscillatory processes may serve to regularize pattern formation, e.g., in chondrogenic condensation in embryonic chicken limbs. They thus contribute to a partial answer to the question: In the feedback between clocks and attraction in swarmalator models, how important is the effect of clocks on attraction? The detailed, systematic comparison of the results of these two types of aggregation is novel. Full article
(This article belongs to the Special Issue Advances in Biological Systems with Mathematics)
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11 pages, 455 KB  
Article
Highly Efficient and Light NTRU-Based Key Encapsulation Mechanisms with Small Moduli
by Jing Fan, Bo-Yue Fang, Wei-Ze Wang, Neng-Hai Yu, Feng-Hua Li and Long Wang
Mathematics 2025, 13(21), 3388; https://doi.org/10.3390/math13213388 (registering DOI) - 24 Oct 2025
Abstract
In this paper, we present CTRU-Light, an IND-CCA-secure key encapsulation mechanism (KEM) derived from NTRU and RLWE (and RLWR in variant) assumptions over power-of-two cyclotomic rings. Our CTRU-Light employs a compact NTT-compatible modulus q=641 while maintaining minimal public key and ciphertext [...] Read more.
In this paper, we present CTRU-Light, an IND-CCA-secure key encapsulation mechanism (KEM) derived from NTRU and RLWE (and RLWR in variant) assumptions over power-of-two cyclotomic rings. Our CTRU-Light employs a compact NTT-compatible modulus q=641 while maintaining minimal public key and ciphertext dimensions with negligible error probability. Specifically, the design yields public key and ciphertext sizes of 1206 bytes under an error probability bound of ≤2−110. When benchmarked against Kyber (NIST’s sole standardized KEM), CTRU-Light demonstrates 23.0–30.0% lower bandwidth consumption, accelerates key generation by at least 6.0%, and achieves over 1.3× speed enhancement in both encapsulation and decapsulation procedures. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
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23 pages, 3174 KB  
Article
A Robust Optimal Control Strategy for PMSM Based on VGPDO and Actor-Critic Neural Network Against Flux Weakening and Mismatched Load Torque
by Yangyu Niu and Haibin Shi
Mathematics 2025, 13(21), 3387; https://doi.org/10.3390/math13213387 - 24 Oct 2025
Abstract
In this paper, a novel robust optimal control strategy is proposed for permanent magnet synchronous motors (PMSMs), simultaneously addressing two critical challenges in speed regulation: flux linkage degradation during long-term operation and abrupt load torque variations. The robust optimal control strategy is implemented [...] Read more.
In this paper, a novel robust optimal control strategy is proposed for permanent magnet synchronous motors (PMSMs), simultaneously addressing two critical challenges in speed regulation: flux linkage degradation during long-term operation and abrupt load torque variations. The robust optimal control strategy is implemented through a combination of feedforward control and feedback control. A novel Variable-Gain Proportional Disturbance Observer (VGPDO) is proposed to simultaneously estimate time-varying flux linkage and torque disturbances in PMSM systems. The estimated disturbances are then compensated via a feedforward control loop, significantly improving the system’s robustness against parameter variations and external load changes. An optimal controller based on an actor-critic neural network provides feedback for optimal control performance. The uniform ultimate boundedness (UUB) of the proposed strategy is proved through Lyapunov stability analysis, and comprehensive simulation studies demonstrate the efficacy of both the proposed VGPDO and the proposed robust optimal control strategy. Full article
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20 pages, 1477 KB  
Article
Dynamic Signal Timing at Urban Intersections: Cycle-Based Delay Classification and Multi-Period Optimization
by Zhao Guo, Alexander Y. Krylatov and Dan Wang
Mathematics 2025, 13(21), 3386; https://doi.org/10.3390/math13213386 - 24 Oct 2025
Abstract
This paper addresses the optimization of traffic signal timing at urban intersections by introducing a dynamic green ratio allocation framework based on cycle-based delay classification. Conventional methods such as the Webster delay model often fail to capture the asymmetric delay characteristics and the [...] Read more.
This paper addresses the optimization of traffic signal timing at urban intersections by introducing a dynamic green ratio allocation framework based on cycle-based delay classification. Conventional methods such as the Webster delay model often fail to capture the asymmetric delay characteristics and the impact of fluctuating flows across multiple cycles. We propose a novel approach that classifies cycles into undersaturated and oversaturated states and develops dedicated optimization models for each type. For undersaturated cycles, a new delay function is derived to accurately capture the interaction between queue dissipation and green time allocation, enabling multi-period minimization of total vehicle delay. For oversaturated cycles, queue minimization at the end of each phase is adopted to accelerate congestion dissipation. The framework is validated through simulation and compared with existing methods, demonstrating superior performance in congestion clearance and delay minimization. The results show improved adaptability to changing traffic conditions and enhanced practicality for real-time signal control in smart transportation systems. Full article
(This article belongs to the Special Issue Optimization and Mathematical Modelling in Transport and Logistics Network)
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22 pages, 2225 KB  
Article
A Chord Error-Priority Bilevel Interpolation Optimization Method for Complex Path Planning
by Pengxuan Wei, Liping Wang, Dan Wang, Jun Qi and Xiaolong Ye
Mathematics 2025, 13(21), 3385; https://doi.org/10.3390/math13213385 - 24 Oct 2025
Abstract
To address path deviation and efficiency reduction issues in traditional interpolation optimization algorithms for complex path machining, this paper proposes a chord error-priority bilevel interpolation optimization method (CPBI). First, arc length parametric modeling of the machining path is performed within the Frenet–Serret framework, [...] Read more.
To address path deviation and efficiency reduction issues in traditional interpolation optimization algorithms for complex path machining, this paper proposes a chord error-priority bilevel interpolation optimization method (CPBI). First, arc length parametric modeling of the machining path is performed within the Frenet–Serret framework, yielding curvature and torsion information. After introducing geometric-based multi-machining constraints in the outer layer, the velocity upper limit is established by controlling chord error to dynamically adjust regions with curvature mutation. In the inner layer, combining the velocity limit with bidirectional scanning achieves adaptive optimization of interpolation step size and optimal velocity planning that balances precision and smoothness. Simulation results demonstrate that CPBI effectively reduces the number of interpolation points by 30–50% while ensuring the chord error. Compared with the reference method, the CPBI improved efficiency by 14.31% and 34.72% in machining experiments on S-shaped and wave-shaped paths, respectively. The results validated the CPBI’s high precision and efficiency advantages in complex path machining, providing an effective solution for CNC path optimization in high-end manufacturing. Full article
(This article belongs to the Special Issue Intelligent Control and Applications of Nonlinear Dynamic System)
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16 pages, 315 KB  
Article
Applications of Bernoulli Polynomials and q2-Srivastava–Attiya Operator in the Study of Bi-Univalent Function Classes
by Basem Aref Frasin, Sondekola Rudra Swamy, Ibtisam Aldawish and Paduvalapattana Kempegowda Mamatha
Mathematics 2025, 13(21), 3384; https://doi.org/10.3390/math13213384 - 24 Oct 2025
Abstract
The central focus of this study is the development and investigation of a generalized subclass of bi-univalent functions, defined using the q2-Srivastava–Attiya operator in conjunction with Bernoulli polynomials. We derive initial coefficient estimates for functions in the newly proposed class and [...] Read more.
The central focus of this study is the development and investigation of a generalized subclass of bi-univalent functions, defined using the q2-Srivastava–Attiya operator in conjunction with Bernoulli polynomials. We derive initial coefficient estimates for functions in the newly proposed class and also provide bounds for the Fekete–Szegö functional. In addition to presenting several new findings, we also explore meaningful connections with previously established results in the theory of bi-univalent and subordinate functions, thereby extending and unifying the existing literature in a novel direction. Full article
(This article belongs to the Special Issue New Trends in Polynomials and Mathematical Analysis)
18 pages, 8743 KB  
Article
Decentralized Tracking Control for Heterogeneous Vehicular Network with Expanding Construction
by Jia-Ke Wang, Jingjing Chu, Yang Liu and Lijie Wang
Mathematics 2025, 13(21), 3383; https://doi.org/10.3390/math13213383 - 23 Oct 2025
Abstract
A decentralized control problem for vehicular platoon systems with heterogeneous dynamic behaviors is investigated in this paper. To simplify the controller design, a longitudinal model is established as an interconnected form. On this basis, a series of decentralized state feedback controllers are designed [...] Read more.
A decentralized control problem for vehicular platoon systems with heterogeneous dynamic behaviors is investigated in this paper. To simplify the controller design, a longitudinal model is established as an interconnected form. On this basis, a series of decentralized state feedback controllers are designed to ensure the individual stability, string stability and connective stability of the vehicular platoon system. Then, a new scenario in which additional vehicles are added to the platoon is also considered by developing an expanding construction system (ECS) based on the proposed longitudinal model. As a result, a corresponding controller can be designed as a new one of the decentralized controllers without changing the original control laws of the interconnected system. The stability conditions are presented with rigorous analysis by virtue of linear matrix inequality (LMI) for the interconnected system and the ECS. Simulation results are carried out to demonstrate the effectiveness of the proposed decentralized tracking controllers. Full article
44 pages, 1049 KB  
Review
Toward Intelligent AIoT: A Comprehensive Survey on Digital Twin and Multimodal Generative AI Integration
by Xiaoyi Luo, Aiwen Wang, Xinling Zhang, Kunda Huang, Songyu Wang, Lixin Chen and Yejia Cui
Mathematics 2025, 13(21), 3382; https://doi.org/10.3390/math13213382 - 23 Oct 2025
Abstract
The Artificial Intelligence of Things (AIoT) is rapidly evolving from basic connectivity to intelligent perception, reasoning, and decision making across domains such as healthcare, manufacturing, transportation, and smart cities. Multimodal generative AI (GAI) and digital twins (DTs) provide complementary solutions. DTs deliver high-fidelity [...] Read more.
The Artificial Intelligence of Things (AIoT) is rapidly evolving from basic connectivity to intelligent perception, reasoning, and decision making across domains such as healthcare, manufacturing, transportation, and smart cities. Multimodal generative AI (GAI) and digital twins (DTs) provide complementary solutions. DTs deliver high-fidelity virtual replicas for real-time monitoring, simulation, and optimization with GAI enhancing cognition, cross-modal understanding, and the generation of synthetic data. This survey presents a comprehensive overview of DT–GAI integration in the AIoT. We review the foundations of DTs and multimodal GAI and highlight their complementary roles. We further introduce the Sense–Map–Generate–Act (SMGA) framework, illustrating their interaction through the SMGA loop. We discuss key enabling technologies, including multimodal data fusion, dynamic DT evolution, and cloud–edge–end collaboration. Representative application scenarios, including smart manufacturing, smart cities, autonomous driving, and healthcare, are examined to demonstrate their practical impact. Finally, we outline open challenges, including efficiency, reliability, privacy, and standardization, and we provide directions for future research toward sustainable, trustworthy, and intelligent AIoT systems. Full article
(This article belongs to the Special Issue New Advances in Distributed Systems, Edge Intelligence, and Artificial Intelligence)
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20 pages, 699 KB  
Article
Analysis of Quantum Multiplicative Calculus and Related Inequalities
by Muhammad Nasim Aftab, Saad Ihsan Butt, Mohammed Alammar and Youngsoo Seol
Mathematics 2025, 13(21), 3381; https://doi.org/10.3390/math13213381 - 23 Oct 2025
Abstract
This article investigates the exact meaning of a quantum derivative result and the corresponding definition of a quantum definite integral in multiplicative calculus from a geometrical viewpoint. After this critical analysis, we give an accurate definition of the q-multiplicative definite integral and [...] Read more.
This article investigates the exact meaning of a quantum derivative result and the corresponding definition of a quantum definite integral in multiplicative calculus from a geometrical viewpoint. After this critical analysis, we give an accurate definition of the q-multiplicative definite integral and the corresponding derivative result. Additionally, an example pertaining to q-multiplicative definite integrals is presented, and rigorous analysis to prove several fundamental results is provided. In addition, two other concepts are defined: the left q-multiplicative derivative and definite integral and the right q-multiplicative derivative and definite integral. Finally, several q-multiplicative Hermite–Hadamard-type inequalities are constructed, and related examples are shown to support our recent findings. Full article
(This article belongs to the Special Issue Current Topics in Optimization, Inequalities and Convex Function Theory)
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15 pages, 313 KB  
Article
Bt-Transformation and Variance Function
by Abdulmajeed Albarrak, Raouf Fakhfakh and Ghadah Alomani
Mathematics 2025, 13(21), 3380; https://doi.org/10.3390/math13213380 (registering DOI) - 23 Oct 2025
Abstract
This study investigates the Bt-transformation of probability measures within the framework of free probability. A primary focus is the invariance under this transformation of two fundamental families: the free Meixner family and the free analog of the Letac–Mora class. In addition, [...] Read more.
This study investigates the Bt-transformation of probability measures within the framework of free probability. A primary focus is the invariance under this transformation of two fundamental families: the free Meixner family and the free analog of the Letac–Mora class. In addition, we introduce novel characteristics associated with the Bt-transformation, offering refined analytical tools to probe its structural and functional properties. These tools allow us to uncover new and significant properties of several distributions in free probability, including the semicircle, the Marchenko–Pastur, and the free Gamma laws, yielding explicit invariance results and stability conditions. Our findings extend the theoretical understanding of the Bt-transformation and provide practical methods for analyzing the dynamics and stability of classical free distributions under this operator. Full article
(This article belongs to the Section D1: Probability and Statistics)
33 pages, 672 KB  
Article
A Laplace Transform-Based Test for Exponentiality Against the EBUCL Class with Applications to Censored and Uncensored Data
by Walid B. H. Etman, Mahmoud E. Bakr, Arwa M. Alshangiti, Oluwafemi Samson Balogun and Rashad M. EL-Sagheer
Mathematics 2025, 13(21), 3379; https://doi.org/10.3390/math13213379 - 23 Oct 2025
Abstract
This paper proposes a novel statistical test for evaluating exponentiality against the recently introduced EBUCL (Exponential Better than Used in Convex Laplace transform order) class of life distributions. The EBUCL class generalizes classical aging concepts and provides a flexible framework for modeling various [...] Read more.
This paper proposes a novel statistical test for evaluating exponentiality against the recently introduced EBUCL (Exponential Better than Used in Convex Laplace transform order) class of life distributions. The EBUCL class generalizes classical aging concepts and provides a flexible framework for modeling various non-exponential aging behaviors. The test is constructed using Laplace transform ordering and is shown to be effective in distinguishing exponential distributions from EBUCL alternatives. We derive the test statistic, establish its asymptotic properties, and assess its performance using Pitman’s asymptotic efficiency under standard alternatives, including Weibull, Makeham, and linear failure rate distributions. Critical values are obtained through extensive Monte Carlo simulations, and the power of the proposed test is evaluated and compared with existing methods. Furthermore, the test is extended to handle right-censored data, demonstrating its robustness and practical applicability. The effectiveness of the procedure is illustrated through several real-world datasets involving both censored and uncensored observations. The results confirm that the proposed test is a powerful and versatile tool for reliability and survival analysis. Full article
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24 pages, 1409 KB  
Article
A Lower-Bounded Extreme Value Distribution for Flood Frequency Analysis with Applications
by Fatimah E. Almuhayfith, Maher Kachour, Amira F. Daghestani, Zahid Ur Rehman, Tassaddaq Hussain and Hassan S. Bakouch
Mathematics 2025, 13(21), 3378; https://doi.org/10.3390/math13213378 - 23 Oct 2025
Abstract
This paper proposes the lower-bounded Fréchet–log-logistic distribution (LFLD), a probability model designed for robust flood frequency analysis (FFA). The LFLD addresses key limitations of traditional distributions (e.g., generalized extreme value (GEV) and log-Pearson Type III (LP3)) by combining bounded support ( [...] Read more.
This paper proposes the lower-bounded Fréchet–log-logistic distribution (LFLD), a probability model designed for robust flood frequency analysis (FFA). The LFLD addresses key limitations of traditional distributions (e.g., generalized extreme value (GEV) and log-Pearson Type III (LP3)) by combining bounded support (α<x<∞) to reflect physical flood thresholds, flexible tail behavior via Fréchet–log-logistic fusion for extreme-value accuracy, and maximum entropy characterization, ensuring optimal parameter estimation. Thus, we obtain the LFLD’s main statistical properties (PDF, CDF, and hazard rate), prove its asymptotic convergence to Fréchet distributions, and validate its superiority through simulation studies showing MLE consistency (bias < 0.02 and mean squared error < 0.0004 for α) and empirical flood data tests (52- and 98-year AMS series), where the LFLD outperforms 10 competitors (AIC reductions of 15–40%; Vuong test p < 0.01). The LFLD’s closed-form quantile function enables efficient return period estimation, critical for infrastructure planning. Results demonstrate its applicability to heavy-tailed, bounded hydrological data, offering a 20–30% improvement in flood magnitude prediction over LP3/GEV models. Full article
(This article belongs to the Special Issue Reliability Estimation and Mathematical Statistics)
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21 pages, 669 KB  
Article
An Elevation-Aware Large-Scale Channel Model for UAV Air-to-Ground Links
by Naier Xia, Yang Liu and Yu Yu
Mathematics 2025, 13(21), 3377; https://doi.org/10.3390/math13213377 - 23 Oct 2025
Abstract
This paper addresses the issue of existing research that fails adequately capture the spatiotemporal nonstationarity caused by the building of occlusion and flight dynamics in air-to-ground channels from unmanned aerial vehicles (UAVs) in urban scenarios. This study focuses on the angular-altitude correlations of [...] Read more.
This paper addresses the issue of existing research that fails adequately capture the spatiotemporal nonstationarity caused by the building of occlusion and flight dynamics in air-to-ground channels from unmanned aerial vehicles (UAVs) in urban scenarios. This study focuses on the angular-altitude correlations of three key metrics: path loss (PL), shadow fading, and the Ricean K-factor. A dynamic path-loss model incorporating the look-down angle is proposed, an exponential decay model for the shadow-fading standard deviation is constructed, and a model for the angle-dependent variation of the Ricean K-factor is established based on line-of-sight probability. Simulations were conducted in two urban-geometry scenarios using WinProp to evaluate the combined effects of flight altitude and elevation angle. The results indicate that path loss decreases and subsequently stabilizes with increasing elevation angle, the shadow-fading standard deviation decreases significantly, and the Ricean K-factor increases with angle and saturates at high angles, in agreement with theoretical predictions. These models are more adaptable to UAV mobility scenarios than traditional fixed exponential models and provide a useful basis for UAV link planning and system optimization in urban environments. Full article
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23 pages, 593 KB  
Article
Enhancing Postpartum Haemorrhage Prediction Through the Integration of Classical Logistic Regression and Machine Learning Algorithms
by Muriel Lérias-Cambeiro, Raquel Mugeiro-Silva, Anabela Rodrigues, Tiago Dias-Domingues, Filipa Lança and António Vaz Carneiro
Mathematics 2025, 13(21), 3376; https://doi.org/10.3390/math13213376 - 23 Oct 2025
Abstract
Postpartum haemorrhage is one of the leading causes of maternal morbidity and mortality worldwide. The early identification of bleeding risk in individual women is crucial for enabling timely interventions and improving patient outcomes.This study aims to evaluate various exploratory and classification methodologies, alongside [...] Read more.
Postpartum haemorrhage is one of the leading causes of maternal morbidity and mortality worldwide. The early identification of bleeding risk in individual women is crucial for enabling timely interventions and improving patient outcomes.This study aims to evaluate various exploratory and classification methodologies, alongside optimisation strategies, for identifying predictors of postpartum haemorrhage. K-means clustering was employed on a retrospective cohort of patients, incorporating demographic, obstetric, and laboratory variables, to delineate patient profiles and select pertinent features. Initially, a classical logistic regression model, implemented without cross-validation, facilitated the identification of six significant predictors for postpartum haemorrhage: lactate dehydrogenase, urea, platelet count, non-O blood group, gestational age, and first-degree lacerations, all of which are variables routinely available in clinical practice. Furthermore, machine learning algorithms—including stepwise logistic regression, ridge logistic regression, and random forest—were utilised, applying cross-validation to optimise predictive performance and enhance generalisability. Among these methodologies, ridge logistic regression emerged as the most effective model, achieving the following metrics: sensitivity 0.857, specificity 0.875, accuracy 0.871, F1-score 0.759, and AUC 0.907. While machine learning techniques demonstrated superior performance, the integration of classical statistical methods with machine learning approaches provides a robust framework for generating reliable predictions and fostering significant clinical insights. Full article
(This article belongs to the Special Issue Advances in Statistics, Biostatistics and Medical Statistics)
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20 pages, 6071 KB  
Article
Study on Gas Pre-Extraction Law of Along-Layer Boreholes Based on Thermo-Hydro-Mechanical-Damage Coupled Model
by Biao Hu, Xuyang Lei, Lu Zhang, Hang Long, Pengfei Ji, Lianmeng Wang, Yonghao Ding and Cuixia Wang
Mathematics 2025, 13(21), 3375; https://doi.org/10.3390/math13213375 - 23 Oct 2025
Abstract
Modeling the pre-extraction of coalbed methane presents a significant mathematical challenge due to the complex interplay of multiple physical fields. This paper presents a robust mathematical model based on a thermo-hydro-mechanical damage (THMD) framework to describe this process. The model is formulated as [...] Read more.
Modeling the pre-extraction of coalbed methane presents a significant mathematical challenge due to the complex interplay of multiple physical fields. This paper presents a robust mathematical model based on a thermo-hydro-mechanical damage (THMD) framework to describe this process. The model is formulated as a system of coupled, non-linear partial differential equations (PDEs) that integrate governing equations for heat transfer, fluid seepage, and solid mechanics with a damage evolution law derived from continuum damage mechanics. A key contribution of this work is the integration of this multi-physics model, solved numerically using the Finite Element Method (FEM), with a statistical modeling approach using Response Surface Methodology (RSM) and Analysis of Variance (ANOVA). This integrated framework allows for a systematic analysis of the model’s parameter space and a rigorous quantification of sensitivities. The ANOVA results reveal that the model’s damage output is most sensitive to the borehole diameter (F = 2531.51), while the effective extraction radius is predominantly governed by the initial permeability (F = 4219.59). This work demonstrates the power of combining a PDE-based multi-physics model with statistical metamodeling to provide deep, quantitative insights for optimizing gas extraction strategies in deep, low-permeability coal seams. Full article
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9 pages, 250 KB  
Article
Counting Rainbow Solutions of a Linear Equation over Fp via Fourier-Analytic Methods
by Francisco-Javier Soto
Mathematics 2025, 13(21), 3374; https://doi.org/10.3390/math13213374 - 23 Oct 2025
Abstract
We study rainbow solutions to linear equations modulo a prime p, where the residue classes are partitioned into n color classes. Using the Fourier method, we derive a universal lower bound that depends only on the class densities and a single spectral [...] Read more.
We study rainbow solutions to linear equations modulo a prime p, where the residue classes are partitioned into n color classes. Using the Fourier method, we derive a universal lower bound that depends only on the class densities and a single spectral parameter: the Fourier bias (the largest nontrivial Fourier coefficient) of each class. When the biases are at the square-root cancellation scale p−1/2 (for random colorings, up to a logp factor), the bound recovers the optimal growth pn−1 with an explicit leading constant and negligible error. Our results complement recent work: in low-bias regimes (pseudorandom or random) they yield sharper quantitative bounds with transparent constants, and the bound requires no extra hypotheses such as coefficient separability. Full article
(This article belongs to the Special Issue Theory and Application of Algebraic Combinatorics, 2nd Edition)
20 pages, 495 KB  
Article
Efficient Single-Server Private Information Retrieval Based on LWE Encryption
by Hai Huang, Zhibo Guan, Bin Yu, Xiang Li, Mengmeng Ge, Chao Ma and Xiangyu Ma
Mathematics 2025, 13(21), 3373; https://doi.org/10.3390/math13213373 - 23 Oct 2025
Abstract
Private Information Retrieval (PIR) is a cryptographic protocol that allows users to retrieve data from one or more databases without revealing any information about their queries. Among existing PIR protocols, single-server schemes based on the Learning With Errors (LWE) assumption currently constitute the [...] Read more.
Private Information Retrieval (PIR) is a cryptographic protocol that allows users to retrieve data from one or more databases without revealing any information about their queries. Among existing PIR protocols, single-server schemes based on the Learning With Errors (LWE) assumption currently constitute the most practical class of constructions. However, existing schemes continue to suffer from high client-side preprocessing complexity and significant server-side storage overhead, leading to degraded overall performance. We propose ShufflePIR, a single-server protocol that marks the first introduction of an SM3-based pseudorandom function into the PIR framework for shuffling during preprocessing and utilizes cryptographic hardware to accelerate computation, thereby improving both efficiency and security. In addition, the adoption of a parallel encryption scheme based on the LWE assumption significantly enhances the client’s computational efficiency when processing long-bit data. We evaluate the performance of our protocol against the latest state-of-the-art PIR schemes. Simulation results demonstrate that ShufflePIR achieves a throughput of 9903 MB/s on a 16 GB database with 1 MB records, outperforming existing single-server PIR schemes. Overall, ShufflePIR provides an efficient and secure solution for privacy-preserving information retrieval in a wide range of applications. Full article
(This article belongs to the Special Issue Mathematical Models in Information Security and Cryptography)
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21 pages, 1214 KB  
Article
Wave Scattering and Trapping by C-Type Floating Breakwaters in the Presence of Bottom-Standing Perforated Semicircular Humps
by Prakash Kar, Harekrushna Behera and Dezhi Ning
Mathematics 2025, 13(21), 3372; https://doi.org/10.3390/math13213372 - 23 Oct 2025
Abstract
In this paper, the propagation of surface gravity waves over multiple bottom-standing porous semicircular humps is examined in the absence and presence of double floating C-type detached asymmetric breakwaters. Both wave scattering and trapping phenomena are investigated within the framework of small-amplitude [...] Read more.
In this paper, the propagation of surface gravity waves over multiple bottom-standing porous semicircular humps is examined in the absence and presence of double floating C-type detached asymmetric breakwaters. Both wave scattering and trapping phenomena are investigated within the framework of small-amplitude linear water wave theory, with the governing problem numerically solved using the multi-domain Boundary Element Method (BEM) in finite-depth water. A detailed parametric analysis is conducted to evaluate the effects of key physical parameters, including hump radius, porosity, spacing between adjacent humps, and the separation between the two C-type detached breakwaters. The study presents results for reflection and transmission coefficients, free-surface elevations, and the horizontal and vertical forces acting on the first perforated semicircular hump, as well as on the shore-fixed wall. The findings highlight the significant role of porous humps in altering Bragg scattering characteristics. For larger wavenumbers, wave reflection increases notably in the presence of a vertical shore-fixed wall, while it tends to vanish in its absence. Reflection is also observed to decrease with an increase in semicircle radius. Furthermore, as the wavenumber approaches zero, the vertical force on multiple permeable semicircles converges to zero, whereas for impermeable semicircles, it approaches unity. In addition, the horizontal force acting on the shore-fixed wall diminishes rapidly with increasing porosity of the semicircular humps. Full article
(This article belongs to the Section E: Applied Mathematics)
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14 pages, 279 KB  
Article
A Hahn-Type Characterization of Generalized Hermite Polynomials Through a Dunkl-Based Raising Operator
by Khalid Ali Alanezy and Jihad Souissi
Mathematics 2025, 13(21), 3371; https://doi.org/10.3390/math13213371 - 23 Oct 2025
Abstract
In this paper, we study Hahn’s problem with respect to a Dunkl-perturbed raising operator. More precisely, we prove that, up to a dilation, the generalized Hermite polynomials are the only Tμ,α-classical symmetric orthogonal polynomials, where [...] Read more.
In this paper, we study Hahn’s problem with respect to a Dunkl-perturbed raising operator. More precisely, we prove that, up to a dilation, the generalized Hermite polynomials are the only Tμ,α-classical symmetric orthogonal polynomials, where Tμ,α=Tμ+αtI, α∈C∖{0} and I denotes the identity operator on the space of polynomials with complex coefficients. The argument uses an operator product rule for Tμ, duality for the associated functionals, and a symmetry-enforced identification together with matching three-term recurrences. The result provides an operator-theoretic Hahn-type characterization that complements semiclassical Pearson-equation descriptions and clarifies the effect of the raising perturbation αtI. Full article
(This article belongs to the Section C: Mathematical Analysis)
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