Mathematics

17 pages, 321 KB

Open AccessArticle

Cyclic, LCD, and Self-Dual Codes over the Non-Frobenius Ring GR(p²,m)[u]/⟨u²,pu⟩

by Sami Alabiad and Alhanouf Ali Alhomaidhi

Mathematics 2025, 13(19), 3193; https://doi.org/10.3390/math13193193 (registering DOI) - 5 Oct 2025

Let p be a prime number and m be a positive integer. In this paper, we investigate cyclic codes of length n over the local non-Frobenius ring

R = G R (p^{2}, m) [u]

, where [...] Read more.

Let p be a prime number and m be a positive integer. In this paper, we investigate cyclic codes of length n over the local non-Frobenius ring

R = G R (p^{2}, m) [u]

, where

u^{2} = 0

and

p u = 0

. We first determine the algebraic structure of cyclic codes of arbitrary length n. For the case

gcd (n, p) = 1

, we explicitly describe the generators of cyclic codes over R. Moreover, we establish necessary and sufficient conditions for the existence of self-dual and LCD codes, together with their enumeration. Several illustrative examples and tables are presented, highlighting the mass formula for cyclic self-orthogonal codes, cyclic LCD codes, and families of new cyclic codes that arise from our results. Full article

28 pages, 3571 KB

Open AccessArticle

Methodology for Transient Stability Assessment and Enhancement in Low-Inertia Power Systems Using Phasor Measurements: A Data-Driven Approach

by Mihail Senyuk, Svetlana Beryozkina, Ismoil Odinaev, Inga Zicmane and Murodbek Safaraliev

Mathematics 2025, 13(19), 3192; https://doi.org/10.3390/math13193192 (registering DOI) - 5 Oct 2025

Abstract

Modern energy systems are undergoing a profound transformation characterized by the active replacement of conventional fossil-fuel-based power plants with renewable energy sources. This transition aims to reduce the carbon emissions associated with electricity generation while enhancing the economic performance of electric power market [...] Read more.

Modern energy systems are undergoing a profound transformation characterized by the active replacement of conventional fossil-fuel-based power plants with renewable energy sources. This transition aims to reduce the carbon emissions associated with electricity generation while enhancing the economic performance of electric power market players. However, alongside these benefits come several challenges, including reduced overall inertia within energy systems, heightened stochastic variability in grid operation regimes, and stricter demands on the rapid response capabilities and adaptability of emergency controls. This paper presents a novel methodology for selecting effective control laws for low-inertia energy systems, ensuring their dynamic stability during post-emergency operational conditions. The proposed approach integrates advanced techniques, including feature selection via decision tree algorithms, classification using Random Forest models, and result visualization through the Mean Shift clustering method applied to a two-dimensional representation derived from the t-distributed Stochastic Neighbor Embedding technique. A modified version of the IEEE39 benchmark model served as the testbed for numerical experiments, achieving a classification accuracy of 98.3%, accompanied by a control law synthesis delay of just 0.047 milliseconds. In conclusion, this work summarizes the key findings and outlines potential enhancements to refine the presented methodology further. Full article

(This article belongs to the Special Issue Mathematical Applications in Electrical Engineering, 2nd Edition)

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18 pages, 1278 KB

Open AccessArticle

MixModel: A Hybrid TimesNet–Informer Architecture with 11-Dimensional Time Features for Enhanced Traffic Flow Forecasting

by Chun-Chi Ting, Kuan-Ting Wu, Hui-Ting Christine Lin and Shinfeng Lin

Mathematics 2025, 13(19), 3191; https://doi.org/10.3390/math13193191 (registering DOI) - 5 Oct 2025

Abstract

The growing demand for reliable long-term traffic forecasting has become increasingly critical in the development of intelligent transportation systems (ITS). However, capturing both strong periodic patterns and long-range temporal dependencies presents a significant challenge, and existing approaches often fail to balance these factors [...] Read more.

The growing demand for reliable long-term traffic forecasting has become increasingly critical in the development of intelligent transportation systems (ITS). However, capturing both strong periodic patterns and long-range temporal dependencies presents a significant challenge, and existing approaches often fail to balance these factors effectively, resulting in unstable or suboptimal predictions. To address this issue, we propose MixModel , a novel hybrid framework that integrates TimesNet and Informer to leverage their complementary strengths. Specifically, the TimesNet branch extracts periodic variations through frequency-domain decomposition and multi-scale convolution, while the Informer branch employs ProbSparse attention to efficiently capture long-range dependencies across extended horizons. By unifying these capabilities, MixModel achieves enhanced forecasting accuracy, robustness, and stability compared with state-of-the-art baselines. Extensive experiments on real-world highway datasets demonstrate the effectiveness of our model, highlighting its potential for advancing large-scale urban traffic management and planning. To the best of our knowledge, MixModel is the first hybrid framework that explicitly bridges frequency-domain periodic modeling and efficient long-range dependency learning for long-term traffic forecasting, establishing a new benchmark for future research in Intelligent Transportation Systems. Full article

40 pages, 458 KB

Open AccessArticle

Large-Number Optimization: Exact-Arithmetic Mathematical Programming with Integers and Fractions Beyond Any Bit Limits

by Josef Kallrath

Mathematics 2025, 13(19), 3190; https://doi.org/10.3390/math13193190 (registering DOI) - 5 Oct 2025

Abstract

Mathematical optimization, in both continuous and discrete forms, is well established and widely applied. This work addresses a gap in the literature by focusing on large-number optimization, where integers or fractions with hundreds of digits occur in decision variables, objective functions, or constraints. [...] Read more.

Mathematical optimization, in both continuous and discrete forms, is well established and widely applied. This work addresses a gap in the literature by focusing on large-number optimization, where integers or fractions with hundreds of digits occur in decision variables, objective functions, or constraints. Such problems challenge standard optimization tools, particularly when exact solutions are required. The suitability of computer algebra systems and high-precision arithmetic software for large-number optimization problems is discussed. Our first contribution is the development of Python implementations of an exact Simplex algorithm and a Branch-and-Bound algorithm for integer linear programming, capable of handling arbitrarily large integers. To test these implementations for correctness, analytic optimal solutions for nine specifically constructed linear, integer linear, and quadratic mixed-integer programming problems are derived. These examples are used to test and verify the developed software and can also serve as benchmarks for future research in large-number optimization. The second contribution concerns constructing partially increasing subsequences of the Collatz sequence. Motivated by this example, we quickly encountered the limits of commercial mixed-integer solvers and instead solved Diophantine equations or applied modular arithmetic techniques to obtain partial Collatz sequences. For any given number J, we obtain a sequence that begins at

2^{J} - 1

and repeats J times the pattern ud: multiply by

3 x_{j} + 1

and then divide by 2. Further partially decreasing sequences are designed, which follow the pattern of multiplying by

3 x_{j} + 1

and then dividing by

2^{m}

. The most general J-times increasing patterns (ududd, udududd, …, ududududddd) are constructed using analytic and semi-analytic methods that exploit modular arithmetic in combination with optimization techniques. Full article

(This article belongs to the Special Issue Innovations in Optimization and Operations Research)

30 pages, 1606 KB

Open AccessArticle

Thermal Entropy Generation in Magnetized Radiative Flow Through Porous Media Over a Stretching Cylinder: An RSM-Based Study

by Shobha Visweswara, Baskar Palani, Fatemah H. H. Al Mukahal, S. Suresh Kumar Raju, Basma Souayeh and Sibyala Vijayakumar Varma

Mathematics 2025, 13(19), 3189; https://doi.org/10.3390/math13193189 (registering DOI) - 5 Oct 2025

Abstract

Magnetohydrodynamic (MHD) flow and heat transfer in porous media are central to many engineering applications, including heat exchangers, MHD generators, and polymer processing. This study examines the boundary layer flow and thermal behavior of an electrically conducting viscous fluid over a porous stretching [...] Read more.

Magnetohydrodynamic (MHD) flow and heat transfer in porous media are central to many engineering applications, including heat exchangers, MHD generators, and polymer processing. This study examines the boundary layer flow and thermal behavior of an electrically conducting viscous fluid over a porous stretching tube. The model accounts for nonlinear thermal radiation, internal heat generation/absorption, and Darcy–Forchheimer drag to capture porous medium resistance. Similarity transformations reduce the governing equations to a system of coupled nonlinear ordinary differential equations, which are solved numerically using the BVP4C technique with Response Surface Methodology (RSM) and sensitivity analysis. The effects of dimensionless parameters magnetic field strength (M), Reynolds number (Re), Darcy–Forchheimer parameter (Df), Brinkman number (Br), Prandtl number (Pr), nonlinear radiation parameter (Rd), wall-to-ambient temperature ratio (rw), and heat source/sink parameter (Q) are investigated. Results show that increasing M, Df, and Q suppresses velocity and enhances temperature due to Lorentz and porous drag effects. Higher Re raises pressure but reduces near-wall velocity, while rw, Rd, and internal heating intensify thermal layers. The entropy generation analysis highlights the competing roles of viscous, magnetic, and thermal irreversibility, while the Bejan number trends distinctly indicate which mechanism dominates under different parameter conditions. The RSM findings highlight that rw and Rd consistently reduce the Nusselt number (Nu), lowering thermal efficiency. These results provide practical guidance for optimizing energy efficiency and thermal management in MHD and porous media-based systems.: Full article

(This article belongs to the Special Issue Advances and Applications in Computational Fluid Dynamics)

30 pages, 793 KB

Open AccessArticle

Integrated Framework of Generalized Interval-Valued Hesitant Intuitionistic Fuzzy Soft Sets with the AHP for Investment Decision-Making Under Uncertainty

by Ema Carnia, Sukono, Moch Panji Agung Saputra, Mugi Lestari, Audrey Ariij Sya’imaa HS, Astrid Sulistya Azahra and Mohd Zaki Awang Chek

Mathematics 2025, 13(19), 3188; https://doi.org/10.3390/math13193188 (registering DOI) - 5 Oct 2025

Abstract

Investment decision-making is often characterized by uncertainty and the subjective weighting of criteria. This study aims to develop a more robust decision support framework by integrating the Generalized Interval-Valued Hesitant Intuitionistic Fuzzy Soft Set (GIVHIFSS) with the Analytic Hierarchy Process (AHP) to objectively [...] Read more.

Investment decision-making is often characterized by uncertainty and the subjective weighting of criteria. This study aims to develop a more robust decision support framework by integrating the Generalized Interval-Valued Hesitant Intuitionistic Fuzzy Soft Set (GIVHIFSS) with the Analytic Hierarchy Process (AHP) to objectively weight criteria and handle multi-evaluator hesitancy. In the proposed GIVHIFSS-AHP model, the AHP is employed to derive mathematically consistent criterion weights, which are subsequently embedded into the GIVHIFSS structure to accommodate interval-valued and hesitant evaluations from multiple decision-makers. The model is applied to a numerical case study evaluating five investment alternatives. Its performance is assessed through a comparative analysis with standard GIVHIFSS and GIFSS models, as well as a sensitivity analysis. The results indicate that the model produces financially rational rankings, identifying blue-chip technology stocks as the optimal choice (score: +2.4). The comparative analysis confirms its superiority over existing models, which yielded less-stable rankings. Moreover, the sensitivity analysis demonstrates the robustness of the results against minor perturbations in criterion weights. This research introduces a novel and synergistic integration of the AHP and GIVHIFSS. The key advantage of this approach lies in its ability to address the long-standing issue of arbitrary criterion weighting in Fuzzy Soft Set models by embedding the AHP as a foundational mechanism for ensuring validation and objectivity. This integration results in mathematically derived, consistent weights, thereby yielding empirically validated, more reliable, and defensible decision outcomes compared with existing models. Full article

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21 pages, 1587 KB

Open AccessFeature PaperArticle

Structure-Preserving Numerical Methods for Fractional Nonlinear Schrödinger Equations with Wave Operators

by Mengnan Zhang, Xinyu Zhou and Cuicui Liao

Mathematics 2025, 13(19), 3187; https://doi.org/10.3390/math13193187 (registering DOI) - 5 Oct 2025

Abstract

This main focus of this work is the fractional-order nonlinear Schrödinger equation with wave operators. First, a conservative difference scheme is constructed. Then, the discrete energy and mass conservation formulas are derived and maintained by the difference scheme constructed in this paper. Through [...] Read more.

This main focus of this work is the fractional-order nonlinear Schrödinger equation with wave operators. First, a conservative difference scheme is constructed. Then, the discrete energy and mass conservation formulas are derived and maintained by the difference scheme constructed in this paper. Through rigorous theoretical analysis, it is proved that the constructed difference scheme is unconditionally stable and has second-order precision in both space and time. Due to the completely implicit property of the differential scheme proposed, a linearized iterative algorithm is proposed to implement the conservative differential scheme. Numerical experiments including one example with the fractional boundary conditions were studied. The results effectively demonstrate the long-term numerical behaviors of the fractional nonlinear Schrödinger equations with wave operators. Full article

(This article belongs to the Section E4: Mathematical Physics)

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12 pages, 1012 KB

Open AccessArticle

Diffraction by Circular Pin: Wiener–Hopf Method

by Seil Sautbekov, Merey Sautbekova and Gulnara Bairova

Mathematics 2025, 13(19), 3186; https://doi.org/10.3390/math13193186 (registering DOI) - 4 Oct 2025

Abstract

In this paper, the boundary value problem of wave diffraction on a semi-infinite circular pin is solved using the Wiener–Hopf method with compensation of eigenmodes. The solution to the problem is presented as an infinite series defined by a recurrence formula. The reliability [...] Read more.

In this paper, the boundary value problem of wave diffraction on a semi-infinite circular pin is solved using the Wiener–Hopf method with compensation of eigenmodes. The solution to the problem is presented as an infinite series defined by a recurrence formula. The reliability and accuracy of the solution are verified numerically in terms of fulfillment of the law of energy conservation. Sufficiently reliable results are obtained at the first iteration. The method used for solving this problem can be applied to solving diffraction problems on axisymmetric volumetric structures. Full article

(This article belongs to the Special Issue Computational Methods in Electromagnetics)

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28 pages, 818 KB

Open AccessArticle

On the Recursive Representation of the Permutation Flow and Job Shop Scheduling Problems and Some Extensions

by Boris Kupriyanov, Alexander Lazarev, Alexander Roschin and Frank Werner

Mathematics 2025, 13(19), 3185; https://doi.org/10.3390/math13193185 (registering DOI) - 4 Oct 2025

Abstract

In this paper, we propose a formulation of the permutation flow and job shop scheduling problems using special recursive functions and show its equivalence to the existing classical formulation. Equivalence is understood in the sense that both ways of defining the problem describe [...] Read more.

In this paper, we propose a formulation of the permutation flow and job shop scheduling problems using special recursive functions and show its equivalence to the existing classical formulation. Equivalence is understood in the sense that both ways of defining the problem describe the same set of feasible schedules for each pair of jobs and machine numbers. In this paper, the apparatus of recursive functions is used to describe and solve three problems: permutation flow shop; permutation flow shop with the addition of the ’and’ predicate extending the machine chain to an acyclic graph; and permutation job shop. The predicate ’and’ allows the description of the flow shop with assembly operation tasks. Recursive functions have a common domain and range. To calculate an optimal schedule for each of these three problems, a branch and bound method is considered based on a recursive function that implements a job swapping algorithm. The complexity of the optimization algorithm does not increase compared to the non-recursive description of the PFSP. This article presents some results for the calculation of optimal schedules on several test instances. It is expected that the new method, based on the description of recursive functions and their superposition, will be productive for formulating and solving some extensions of scheduling problems that have practical significance. Full article

(This article belongs to the Special Issue Innovations in Optimization and Operations Research)

22 pages, 48967 KB

Open AccessArticle

Parametric Blending with Geodesic Curves on Triangular Meshes

by Seong-Hyeon Kweon, Seung-Yong Lee and Seung-Hyun Yoon

Mathematics 2025, 13(19), 3184; https://doi.org/10.3390/math13193184 (registering DOI) - 4 Oct 2025

Abstract

This paper presents an effective method for generating blending meshes by leveraging geodesic curves on triangular meshes. Depending on whether the input meshes intersect, the blending regions are automatically initialized using either minimum-distance points or intersection curves, while allowing users to intuitively adjust [...] Read more.

This paper presents an effective method for generating blending meshes by leveraging geodesic curves on triangular meshes. Depending on whether the input meshes intersect, the blending regions are automatically initialized using either minimum-distance points or intersection curves, while allowing users to intuitively adjust boundary curves directly on the mesh. Each blending region is parameterized via geodesic linear interpolation, and a reparameterization strategy is employed to establish optimal correspondences between boundary curves, ensuring smooth, twist-free connections. The resulting blending mesh is merged with the input meshes through subdivision, trimming, and co-refinement along the boundaries. The proposed method is applicable to both intersecting and non-intersecting meshes and offers flexible control over the shape and curvature of the blending region through various user-defined parameters, such as boundary radius, scaling factor, and blending function parameters. Experimental results demonstrate that the method produces stable and smooth transitions even for complex geometries, highlighting its robustness and practical applicability in diverse domains including digital fabrication, mechanical design, and 3D object modeling. Full article

(This article belongs to the Special Issue Mathematical Applications in Computer Graphics)

18 pages, 5180 KB

Open AccessArticle

Efficient 3D Model Simplification Algorithms Based on OpenMP

by Han Chang, Sanhe Wan, Jingyu Ni, Yidan Fan, Xiangxue Zhang and Yuxuan Xiong

Mathematics 2025, 13(19), 3183; https://doi.org/10.3390/math13193183 (registering DOI) - 4 Oct 2025

Abstract

Efficient simplification of 3D models is essential for mobile and other resource-constrained application scenarios. Industrial 3D assemblies, typically composed of numerous components and dense triangular meshes, often pose significant challenges in rendering and transmission due to their large scale and high complexity. The [...] Read more.

Efficient simplification of 3D models is essential for mobile and other resource-constrained application scenarios. Industrial 3D assemblies, typically composed of numerous components and dense triangular meshes, often pose significant challenges in rendering and transmission due to their large scale and high complexity. The Quadric Error Metrics (QEM) algorithm offers a practical balance between simplification accuracy and computational efficiency. However, its application to large-scale industrial models remain limited by performance bottlenecks, especially when combined with curvature-based optimization techniques that improve fidelity at the cost of increased computation. Therefore, this paper presents a parallel implementation of the QEM algorithm and its curvature-optimized variant using the OpenMP framework. By identifying key bottlenecks in the serial workflow, this research parallelizes critical processes such as curvature estimation, error metric computation, and data structure manipulation. Experiments on large industrial assembly models at a simplification ratio of 0.3, 0.5, and 0.7 demonstrate that the proposed parallel algorithms achieve significant speedups, with a maximum observed speedup of 5.5×, while maintaining geometric quality and topological consistency. The proposed approach significantly improves model processing efficiency, particularly for medium- to large-scale industrial models, and provides a scalable and practical solution for real-time loading and interaction in engineering applications. Full article

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18 pages, 837 KB

Open AccessArticle

Physics-Informed Feature Engineering and R²-Based Signal-to-Noise Ratio Feature Selection to Predict Concrete Shear Strength

by Trevor J. Bihl, William A. Young II and Adam Moyer

Mathematics 2025, 13(19), 3182; https://doi.org/10.3390/math13193182 (registering DOI) - 4 Oct 2025

Abstract

Accurate prediction of reinforced concrete shear strength is essential for structural safety, yet datasets often contain a mix of raw geometric and material properties alongside physics-informed engineered features, making optimal feature selection challenging. This study introduces a statistically principled framework that advances feature [...] Read more.

Accurate prediction of reinforced concrete shear strength is essential for structural safety, yet datasets often contain a mix of raw geometric and material properties alongside physics-informed engineered features, making optimal feature selection challenging. This study introduces a statistically principled framework that advances feature reduction for neural networks in three novel ways. First, it extends the artificial neural network-based signal-to-noise ratio (ANN-SNR) method, previously limited to classification, into regression tasks for the first time. Second, it couples ANN-SNR with a confidence-interval (CI)-based stopping rule, using the lower bound of the baseline ANN’s R² confidence interval as a rigorous statistical threshold for determining when feature elimination should cease. Third, it systematically evaluates both raw experimental variables and physics-informed engineered features, showing how their combination enhances both robustness and interpretability. Applied to experimental concrete shear strength data, the framework revealed that many low-SNR features in conventional formulations contribute little to predictive performance and can be safely removed. In contrast, hybrid models that combined key raw and engineered features consistently yielded the strongest performance. Overall, the proposed method reduced the input feature set by approximately 45% while maintaining results statistically indistinguishable from baseline and fully optimized models (R² ≈ 0.85). These findings demonstrate that ANN-SNR with CI-based stopping provides a defensible and interpretable pathway for reducing model complexity in reinforced concrete shear strength prediction, offering practical benefits for design efficiency without compromising reliability. Full article

18 pages, 14342 KB

Open AccessArticle

A Multi-LiDAR Self-Calibration System Based on Natural Environments and Motion Constraints

by Yuxuan Tang, Jie Hu, Zhiyong Yang, Wencai Xu, Shuaidi He and Bolun Hu

Mathematics 2025, 13(19), 3181; https://doi.org/10.3390/math13193181 (registering DOI) - 4 Oct 2025

Abstract

Autonomous commercial vehicles often mount multiple LiDARs to enlarge their field of view, but conventional calibration is labor-intensive and prone to drift during long-term operation. We present an online self-calibration method that combines a ground plane motion constraint with a virtual RGB–D projection, [...] Read more.

Autonomous commercial vehicles often mount multiple LiDARs to enlarge their field of view, but conventional calibration is labor-intensive and prone to drift during long-term operation. We present an online self-calibration method that combines a ground plane motion constraint with a virtual RGB–D projection, mapping 3D point clouds to 2D feature/depth images to reduce feature extraction cost while preserving 3D structure. Motion consistency across consecutive frames enables a reduced-dimension hand–eye formulation. Within this formulation, the estimation integrates geometric constraints on

S E (3)

using Lagrange multiplier aggregation and quasi-Newton refinement. This approach highlights key aspects of identifiability, conditioning, and convergence. An online monitor evaluates plane alignment and LiDAR–INS odometry consistency to detect degradation and trigger recalibration. Tests on a commercial vehicle with six LiDARs and on nuScenes demonstrate accuracy comparable to offline, target-based methods while supporting practical online use. On the vehicle, maximum errors are 6.058 cm (translation) and 4.768° (rotation); on nuScenes, 2.916 cm and 5.386°. The approach streamlines calibration, enables online monitoring, and remains robust in real-world settings. Full article

(This article belongs to the Section A: Algebra and Logic)

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24 pages, 2014 KB

Open AccessArticle

Multi-Agent Reinforcement Learning with Two-Layer Control Plane for Traffic Engineering

by Evgeniy Stepanov, Ruslan Smeliansky and Ivan Garkavy

Mathematics 2025, 13(19), 3180; https://doi.org/10.3390/math13193180 - 3 Oct 2025

Abstract

The article presents a new method for multi-agent traffic flow balancing. It is based on the MAROH multi-agent optimization method. However, unlike MAROH, the agent’s control plane is built on the principles of human decision-making and consists of two layers. The first layer [...] Read more.

The article presents a new method for multi-agent traffic flow balancing. It is based on the MAROH multi-agent optimization method. However, unlike MAROH, the agent’s control plane is built on the principles of human decision-making and consists of two layers. The first layer ensures autonomous decision-making by the agent based on accumulated experience—representatives of states the agent has encountered and knows which actions to take in them. The second layer enables the agent to make decisions for unfamiliar states. A state is considered familiar to the agent if it is close, in terms of a specific metric, to a state the agent has already encountered. The article explores variants of state proximity metrics and various ways to organize the agent’s memory. It has been experimentally shown that an agent with the proposed two-layer control plane SAMAROH-2L outperforms the efficiency of an agent with a single-layer control plane, e.g., makes decisions faster, and inter-agent communication reduction varies from 1% to 80% depending on the selected similarity threshold comparing the method with simultaneous actions SAMAROH and from 80% to 96% comparing to MAROH. Full article

(This article belongs to the Special Issue Applications of Cloud Computing, Big Data, and Data Dissemination in Information Engineering)

26 pages, 2586 KB

Open AccessArticle

Equilibrium Dynamics in the CR3BP with Radiating Primary and Oblate Secondary Using the Rotating Mass Dipole Model

by Angela E. Perdiou, Aguda Ekele Vincent, Jagadish Singh and Vassilis S. Kalantonis

Mathematics 2025, 13(19), 3179; https://doi.org/10.3390/math13193179 - 3 Oct 2025

Abstract

In this study, we numerically investigate the equilibrium dynamics of a rotating system consisting of two masses connected by a massless rod within the framework of the circular restricted three-body problem. The larger primary is modeled as a radiating body and the smaller [...] Read more.

In this study, we numerically investigate the equilibrium dynamics of a rotating system consisting of two masses connected by a massless rod within the framework of the circular restricted three-body problem. The larger primary is modeled as a radiating body and the smaller as an oblate spheroid. We explore the influence of the involved parameters, i.e., mass ratio (

μ

), force ratio (k), radiation pressure factor (

q_{1}

), and oblateness coefficient (

A_{2}

), on the number, positions, and linear stability of equilibrium points. Zero velocity curves are presented in the equatorial plane for varying values of the Jacobi constant. Up to five equilibrium points are identified of which three are collinear (

L_{1}

,

L_{2}

,

L_{3}

) and two are non-collinear (

L_{4}

,

L_{5}

). The positions of all equilibria shift under variations in the perturbing parameters. While the collinear points are generally unstable,

L_{1}

can exhibit stability for certain combinations of

μ

, k, and

q_{1}

. The non-collinear points may also be stable under specific conditions with stability zones expanding with increased parameter values. The model is applied to the irregular, elongated asteroid 951 Gaspra, for which five equilibrium points are found. Despite positional dependence on oblateness and radiation, the perturbations do not significantly affect the equilibrium points’ stability and the motion near them remains linearly unstable. The Lyapunov families of periodic orbits emanating from the collinear equilibria of this particular system are also investigated. Full article

(This article belongs to the Section C2: Dynamical Systems)

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22 pages, 1056 KB

Open AccessArticle

Trajectory Tracking of WMR with Neural Adaptive Correction

by Sahbi Boubaker, Jeremias Gaia, Eduardo Zavalla, Souad Kamel, Faisal S. Alsubaei, Farid Bourennani and Francisco Rossomando

Mathematics 2025, 13(19), 3178; https://doi.org/10.3390/math13193178 - 3 Oct 2025

Abstract

Wheeled mobile robots (WMRs) are being increasingly integrated into various sectors such as logistics and transportation. However, their accurate trajectory tracking remains a challenge. To address this control issue, this study proposes a trajectory correction technique for a wheeled mobile robot (WMR). This [...] Read more.

Wheeled mobile robots (WMRs) are being increasingly integrated into various sectors such as logistics and transportation. However, their accurate trajectory tracking remains a challenge. To address this control issue, this study proposes a trajectory correction technique for a wheeled mobile robot (WMR). This proposal uses a functional-link neural network (FLNN) that adjusts the trajectory error with the aim of minimizing it. This error is propagated backward by adjusting the different parameters of the controller. The controller was designed using a combination of linearization feedback, sliding mode control, and FLNN, where the latter provides adaptability to the controller. Using the Lyapunov stability theory, the stability of the proposal was demonstrated. Experiments and simulation analyses were also carried out to demonstrate the practical feasibility of the proposal. Full article

(This article belongs to the Section C2: Dynamical Systems)

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10 pages, 231 KB

Open AccessFeature PaperArticle

Composition of Activation Functions and the Reduction to Finite Domain

by George A. Anastassiou

Mathematics 2025, 13(19), 3177; https://doi.org/10.3390/math13193177 - 3 Oct 2025

Abstract

This work takes up the task of the determination of the rate of pointwise and uniform convergences to the unit operator of the “normalized cusp neural network operators”. The cusp is a compact support activation function, which is the composition of two general [...] Read more.

This work takes up the task of the determination of the rate of pointwise and uniform convergences to the unit operator of the “normalized cusp neural network operators”. The cusp is a compact support activation function, which is the composition of two general activation functions having as domain the whole real line. These convergences are given via the modulus of continuity of the engaged function or its derivative in the form of Jackson type inequalities. The composition of activation functions aims to more flexible and powerful neural networks, introducing for the first time the reduction in infinite domains to the one domain of compact support. Full article

(This article belongs to the Special Issue Special Functions with Applications)

31 pages, 9679 KB

Open AccessFeature PaperArticle

Weather-Corrupted Image Enhancement with Removal-Raindrop Diffusion and Mutual Image Translation Modules

by Young-Ho Go and Sung-Hak Lee

Mathematics 2025, 13(19), 3176; https://doi.org/10.3390/math13193176 - 3 Oct 2025

Abstract

Artificial intelligence-based image processing is critical for sensor fusion and image transformation in mobility systems. Advanced driver assistance functions such as forward monitoring and digital side mirrors are essential for driving safety. Degradation due to raindrops, fog, and high-dynamic range (HDR) imbalance caused [...] Read more.

Artificial intelligence-based image processing is critical for sensor fusion and image transformation in mobility systems. Advanced driver assistance functions such as forward monitoring and digital side mirrors are essential for driving safety. Degradation due to raindrops, fog, and high-dynamic range (HDR) imbalance caused by lighting changes impairs visibility and reduces object recognition and distance estimation accuracy. This paper proposes a diffusion framework to enhance visibility under multi-degradation conditions. The denoising diffusion probabilistic model (DDPM) offers more stable training and high-resolution restoration than the generative adversarial networks. The DDPM relies on large-scale paired datasets, which are difficult to obtain in raindrop scenarios. This framework applies the Palette diffusion model, comprising data augmentation and raindrop-removal modules. The data augmentation module generates raindrop image masks and learns inpainting-based raindrop synthesis. Synthetic masks simulate raindrop patterns and HDR imbalance scenarios. The raindrop-removal module reconfigures the Palette architecture for image-to-image translation, incorporating the augmented synthetic dataset for raindrop removal learning. Loss functions and normalization strategies improve restoration stability and removal performance. During inference, the framework operates with a single conditional input, and an efficient sampling strategy is introduced to significantly accelerate the process. In post-processing, tone adjustment and chroma compensation enhance visual consistency. The proposed method preserves fine structural details and outperforms existing approaches in visual quality, improving the robustness of vision systems under adverse conditions. Full article

(This article belongs to the Special Issue Deep Learning in Image Processing and Scientific Computing)

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24 pages, 462 KB

Open AccessArticle

New Results on the Computation of Periods of IETs

by Antonio Linero Bas and Gabriel Soler López

Mathematics 2025, 13(19), 3175; https://doi.org/10.3390/math13193175 - 3 Oct 2025

Abstract

We introduce a novel technique for computing the periods of

(d, k)

-IETs based on Rauzy induction

R

. Specifically, we establish a connection between the set of periods of an interval exchange transformation (IET) T and those of the [...] Read more.

We introduce a novel technique for computing the periods of

(d, k)

-IETs based on Rauzy induction

R

. Specifically, we establish a connection between the set of periods of an interval exchange transformation (IET) T and those of the IET

T^{'}

obtained either by applying the Rauzy operator

R

to T or by considering the Poincaré first return map. Rauzy matrices play a central role in this correspondence whenever T lies in the domain of

R

(Theorem 4). Furthermore, Theorem 6 addresses the case when T is not in the domain of

R

, while Theorem 5 deals with IETs having associated reducible permutations. As an application, we characterize the set of periods of oriented 3-IETs (Theorem 8), and we also propose a general framework for studying the periods of

(d, k)

-IETs. Our approach provides a systematic method for determining the periods of non-transitive IETs. In general, given an IET with d discontinuities, if Rauzy induction allows us to descend to another IET whose periodic components are already known, then the main theorems of this paper can be applied to recover the set of periods of the original IET. This method has been also applied to obtain the set of periods of all

(2, k)

-IETs and some

(3, k)

-IETs,

k \geq 1

. Several open problems are presented at the end of the paper. Full article

(This article belongs to the Section C2: Dynamical Systems)

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