Mathematics

42 pages, 8362 KiB

Open AccessArticle

Mathematical Modeling of Signals for Weight Control of Vehicles Using Seismic Sensors

by Nikita V. Martyushev, Boris V. Malozyomov, Anton Y. Demin, Alexander V. Pogrebnoy, Egor A. Efremenkov, Denis V. Valuev and Aleksandr E. Boltrushevich

Mathematics 2025, 13(13), 2083; https://doi.org/10.3390/math13132083 - 24 Jun 2025

Abstract

The article presents a new method of passive dynamic weighing of vehicles based on the registration of seismic signals that occur when wheels pass through strips specially applied to the road surface. Signal processing is carried out using spectral methods, including fast Fourier [...] Read more.

The article presents a new method of passive dynamic weighing of vehicles based on the registration of seismic signals that occur when wheels pass through strips specially applied to the road surface. Signal processing is carried out using spectral methods, including fast Fourier transform, consistent filtering, and regularization methods for solving inverse problems. Special attention is paid to the use of linear-frequency-modulated signals, which make it possible to distinguish the responses of individual axes even when superimposed. Field tests were carried out on a real section of the road, during which signals from vehicles of various classes were recorded using eight geophones. The average error in determining the speed of 1.2 km/h and the weight of 8.7% was experimentally achieved, while the correct determination of the number of axles was 96.5%. The results confirm the high accuracy and sustainability of the proposed approach with minimal implementation costs. It is shown that this system can be scaled up for use in intelligent transport systems and applied in real traffic conditions without the need to intervene in the design of the roadway. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 3rd Edition)

24 pages, 439 KiB

Open AccessFeature PaperArticle

Faithful Tropicalization and Skeleton of M¯_0,n

by Jiachang Xu and Muyuan Zhang

Mathematics 2025, 13(13), 2082; https://doi.org/10.3390/math13132082 - 24 Jun 2025

Abstract

We propose a new method to compare between the essential skeleton of Berkovich analytification of

({\bar{M}}_{0, n}, {\bar{M}}_{0, n} ∖ M_{0, n})

and faithful tropicalization of

M_{0, n}

over a [...] Read more.

We propose a new method to compare between the essential skeleton of Berkovich analytification of

({\bar{M}}_{0, n}, {\bar{M}}_{0, n} ∖ M_{0, n})

and faithful tropicalization of

M_{0, n}

over a complete discrete valued field. In particular, we proved the two combinatorial structures are the same in terms of valuation in

{\bar{M}}_{0, n}^{an}

. Full article

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

18 pages, 1198 KiB

Open AccessFeature PaperArticle

Information-Theoretic Sequential Framework to Elicit Dynamic High-Order Interactions in High-Dimensional Network Processes

by Helder Pinto, Yuri Antonacci, Gorana Mijatovic, Laura Sparacino, Sebastiano Stramaglia, Luca Faes and Ana Paula Rocha

Mathematics 2025, 13(13), 2081; https://doi.org/10.3390/math13132081 - 24 Jun 2025

Abstract

Complex networks of stochastic processes are crucial for modeling the dynamics of interacting systems, particularly those involving high-order interactions (HOIs) among three or more components. Traditional measures—such as mutual information (MI), interaction information (II), the redundancy-synergy index (RSI), and O-information (OI)—are typically limited [...] Read more.

Complex networks of stochastic processes are crucial for modeling the dynamics of interacting systems, particularly those involving high-order interactions (HOIs) among three or more components. Traditional measures—such as mutual information (MI), interaction information (II), the redundancy-synergy index (RSI), and O-information (OI)—are typically limited to static analyses not accounting for temporal correlations and become computationally unfeasible in large networks due to the exponential growth of the number of interactions to be analyzed. To address these challenges, first a framework is introduced to extend these information-theoretic measures to dynamic processes. This includes the II rate (IIR), RSI rate (RSIR), and the OI rate gradient (ΔOIR), enabling the dynamic analysis of HOIs. Moreover, a stepwise strategy identifying groups of nodes (multiplets) that maximize either redundant or synergistic HOIs is devised, offering deeper insights into complex interdependencies. The framework is validated through simulations of networks composed of cascade, common drive, and common target mechanisms, modelled using vector autoregressive (VAR) processes. The feasibility of the proposed approach is demonstrated through its application in climatology, specifically by analyzing the relationships between climate variables that govern El Niño and the Southern Oscillation (ENSO) using historical climate data. Full article

(This article belongs to the Special Issue Recent Advances in Time Series Analysis)

23 pages, 330 KiB

Open AccessFeature PaperArticle

PageRank of Gluing Networks and Corresponding Markov Chains

by Xuqian Ben Han, Shihao Wang and Chenglong Yu

Mathematics 2025, 13(13), 2080; https://doi.org/10.3390/math13132080 - 24 Jun 2025

Abstract

This paper studies Google’s PageRank algorithm. By an innovative application of the method of gluing Markov chains, we study the properties of Markov chains and extend their applicability by accounting for the damping factor and the personalization vector. Many properties of Markov chains [...] Read more.

This paper studies Google’s PageRank algorithm. By an innovative application of the method of gluing Markov chains, we study the properties of Markov chains and extend their applicability by accounting for the damping factor and the personalization vector. Many properties of Markov chains related to spectrums and eigenvectors of the transition matrix, including the stationary distribution, periodicity, and persistent and transient states, will be investigated as well as part of the gluing process. Using the gluing formula, it is possible to decompose a large network into some sub-networks, compute their PageRank separably and glue them together. The computational workload can be reduced. Full article

(This article belongs to the Section E: Applied Mathematics)

37 pages, 20758 KiB

Open AccessReview

A Comprehensive Review of Image Restoration Research Based on Diffusion Models

by Jun Li, Heran Wang, Yingjie Li and Haochuan Zhang

Mathematics 2025, 13(13), 2079; https://doi.org/10.3390/math13132079 - 24 Jun 2025

Abstract

Image restoration is an indispensable and challenging task in computer vision, aiming to enhance the quality of images degraded by various forms of degradation. Diffusion models have achieved remarkable progress in AIGC (Artificial Intelligence Generated Content) image generation, and numerous studies have explored [...] Read more.

Image restoration is an indispensable and challenging task in computer vision, aiming to enhance the quality of images degraded by various forms of degradation. Diffusion models have achieved remarkable progress in AIGC (Artificial Intelligence Generated Content) image generation, and numerous studies have explored their application in image restoration, achieving performance surpassing that of other methods. This paper provides a comprehensive overview of diffusion models for image restoration, starting with an introduction to the background of diffusion models. It summarizes relevant theories and research in utilizing diffusion models for image restoration in recent years, elaborating on six commonly used methods and their unified paradigm. Based on these six categories, this paper classifies restoration tasks into two main areas: image super-resolution reconstruction and frequency-selective image restoration. The frequency-selective image restoration category includes image deblurring, image inpainting, image deraining, image desnowing, image dehazing, image denoising, and low-light enhancement. For each area, this paper delves into the technical principles and modeling strategies. Furthermore, it analyzes the specific characteristics and contributions of the diffusion models employed in each application category. This paper summarizes commonly used datasets and evaluation metrics for these six applications to facilitate comprehensive evaluation of existing methods. Finally, it concludes by identifying the limitations of current research, outlining challenges, and offering perspectives on future applications. Full article

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25 pages, 4507 KiB

Open AccessArticle

Adaptive Dynamic Programming-Based Intelligent Finite-Time Flexible SMC for Stabilizing Fractional-Order Four-Wing Chaotic Systems

by Mai The Vu, Seong Han Kim, Duc Hung Pham, Ha Le Nhu Ngoc Thanh, Van Huy Pham and Majid Roohi

Mathematics 2025, 13(13), 2078; https://doi.org/10.3390/math13132078 - 24 Jun 2025

Abstract

Fractional-order four-wing (FO 4-wing) systems are of significant importance due to their complex dynamics and wide-ranging applications in secure communications, encryption, and nonlinear circuit design, making their control and stabilization a critical area of study. In this research, a novel model-free finite-time flexible [...] Read more.

Fractional-order four-wing (FO 4-wing) systems are of significant importance due to their complex dynamics and wide-ranging applications in secure communications, encryption, and nonlinear circuit design, making their control and stabilization a critical area of study. In this research, a novel model-free finite-time flexible sliding mode control (FTF-SMC) strategy is developed for the stabilization of a particular category of hyperchaotic FO 4-wing systems, which are subject to unknown uncertainties and input saturation constraints. The proposed approach leverages fractional-order Lyapunov stability theory to design a flexible sliding mode controller capable of effectively addressing the chaotic dynamics of FO 4-wing systems and ensuring finite-time convergence. Initially, a dynamic sliding surface is formulated to accommodate system variations. Following this, a robust model-free control law is designed to counteract uncertainties and input saturation effects. The finite-time stability of both the sliding surface and the control scheme is rigorously proven. The control strategy eliminates the need for explicit system models by exploiting the norm-bounded characteristics of chaotic system states. To optimize the parameters of the model-free FTF-SMC, a deep reinforcement learning framework based on the adaptive dynamic programming (ADP) algorithm is employed. The ADP agent utilizes two neural networks (NNs)—action NN and critic NN—aiming to obtain the optimal policy by maximizing a predefined reward function. This ensures that the sliding motion satisfies the reachability condition within a finite time frame. The effectiveness of the proposed methodology is validated through comprehensive simulations, numerical case studies, and comparative analyses. Full article

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36 pages, 5420 KiB

Open AccessArticle

Modeling Porosity Distribution Strategies in PEM Water Electrolyzers: A Comparative Analytical and Numerical Study

by Ali Bayat, Prodip K. Das and Suvash C. Saha

Mathematics 2025, 13(13), 2077; https://doi.org/10.3390/math13132077 - 23 Jun 2025

Abstract

Proton exchange membrane water electrolyzers (PEMWEs) are a promising technology for green hydrogen production. However, the adoption of PEMWE-based hydrogen production systems remains limited due to several challenges, including high material costs, limited performance and durability, and difficulties in scaling the technology. Computational [...] Read more.

Proton exchange membrane water electrolyzers (PEMWEs) are a promising technology for green hydrogen production. However, the adoption of PEMWE-based hydrogen production systems remains limited due to several challenges, including high material costs, limited performance and durability, and difficulties in scaling the technology. Computational modeling serves as a powerful tool to address these challenges by optimizing system design, improving material performance, and reducing overall costs, thereby accelerating the commercial rollout of PEMWE technology. Despite this, conventional models often oversimplify key components, such as porous transport and catalyst layers, by assuming constant porosity and neglecting the spatial heterogeneity found in real electrodes. This simplification can significantly impact the accuracy of performance predictions and the overall efficiency of electrolyzers. This study develops a mathematical framework for modeling variable porosity distributions—including constant, linearly graded, and stepwise profiles—and derives analytical expressions for permeability, effective diffusivity, and electrical conductivity. These functions are integrated into a three-dimensional multi-domain COMSOL simulation to assess their impact on electrochemical performance and transport behavior. The results reveal that although porosity variations have minimal effect on polarization at low voltages, they significantly influence internal pressure, species distribution, and gas evacuation at higher loads. A notable finding is that reversing stepwise porosity—placing high porosity near the membrane rather than the channel—can alleviate oxygen accumulation and improve current density. A multi-factor comparison highlights this reversed configuration as the most favorable among the tested strategies. The proposed modeling approach effectively connects porous media theory and system-level electrochemical analysis, offering a flexible platform for the future design of porous electrodes in PEMWE and other energy conversion systems. Full article

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2 pages, 139 KiB

Open AccessEditorial

Editorial for the Special Issue “Mathematical Developments in Modeling Current Financial Phenomena”

by Camelia Oprean-Stan and Voichița Adriana Radu

Mathematics 2025, 13(13), 2076; https://doi.org/10.3390/math13132076 - 23 Jun 2025

Abstract

Systemic challenges, behavioral complexities, and rapid technological integration have all contributed to the astonishing pace of change in the global financial landscape [...] Full article

(This article belongs to the Special Issue Mathematical Developments in Modeling Current Financial Phenomena)

14 pages, 771 KiB

Open AccessArticle

Valuation of Euro-Convertible Bonds in a Markov-Modulated, Cox–Ingersoll–Ross Economy

by Yu-Min Lian, Jun-Home Chen and Szu-Lang Liao

Mathematics 2025, 13(13), 2075; https://doi.org/10.3390/math13132075 - 23 Jun 2025

Abstract

This study investigates the valuation of Euro-convertible bonds (ECBs) using a novel Markov-modulated cojump-diffusion (MMCJD) model, which effectively captures the dynamics of stochastic volatility and simultaneous jumps (cojumps) in both the underlying stock prices and foreign exchange (FX) rates. Furthermore, we introduce a [...] Read more.

This study investigates the valuation of Euro-convertible bonds (ECBs) using a novel Markov-modulated cojump-diffusion (MMCJD) model, which effectively captures the dynamics of stochastic volatility and simultaneous jumps (cojumps) in both the underlying stock prices and foreign exchange (FX) rates. Furthermore, we introduce a Markov-modulated Cox–Ingersoll–Ross (MMCIR) framework to accurately model domestic and foreign instantaneous interest rates within a regime-switching environment. To manage computational complexity, the least-squares Monte Carlo (LSMC) approach is employed for estimating ECB values. Numerical analyses demonstrate that explicitly incorporating stochastic volatilities and cojumps significantly enhances the realism of ECB pricing, underscoring the novelty and contribution of our integrated modeling approach. Full article

(This article belongs to the Special Issue Advanced Research in Mathematical Economics and Financial Modelling, 2nd Edition)

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34 pages, 4558 KiB

Open AccessArticle

Neuro-Driven Agent-Based Security for Quantum-Safe 6G Networks

by Mohammed Alwakeel

Mathematics 2025, 13(13), 2074; https://doi.org/10.3390/math13132074 - 23 Jun 2025

Abstract

Around the same time that 6G networks will be launched, advances in quantum computing could challenge existing cryptographic security. This study provides a new approach for designing a quantum-safe 6G security architecture powered by neurons. The framework uses connected cognitive agents that apply [...] Read more.

Around the same time that 6G networks will be launched, advances in quantum computing could challenge existing cryptographic security. This study provides a new approach for designing a quantum-safe 6G security architecture powered by neurons. The framework uses connected cognitive agents that apply neuro-symbolic learning to respond quickly to any quantum-based security threats that may appear in network slices. Experiments carried out using simulations across various network setups with different threats verify that the presented method improves the detection rate of quantum attacks by 37.8%, uses 29.2% less communication capacity than other methods in the field. This network includes features that strengthen it to resist quantum decryption, while at the same time keeping replies fast enough for 6G. When using specific quantum-inspired techniques, accomplishing tasks requires only 42.5% fewer false alarms compared to other intrusion methods. With this research, people are now better prepared for quantum-protected wireless networks and 6G systems that ensure stability in the future. Full article

(This article belongs to the Special Issue Application of Artificial Intelligence in Decision Making)

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24 pages, 1601 KiB

Open AccessArticle

Finding the q-Appell Convolution of Certain Polynomials Within the Context of Quantum Calculus

by Waseem Ahmad Khan, Khidir Shaib Mohamed, Francesco Aldo Costabile, Can Kızılateş and Cheon Seoung Ryoo

Mathematics 2025, 13(13), 2073; https://doi.org/10.3390/math13132073 - 23 Jun 2025

Abstract

This article introduces the theory of three-variable q-truncated exponential Gould–Hopper-based Appell polynomials by employing a generating function approach that incorporates q-calculus functions. This study further explores these polynomials by using a computational algebraic approach. The determinant form, recurrences, and differential equations [...] Read more.

This article introduces the theory of three-variable q-truncated exponential Gould–Hopper-based Appell polynomials by employing a generating function approach that incorporates q-calculus functions. This study further explores these polynomials by using a computational algebraic approach. The determinant form, recurrences, and differential equations are proven. Relationships with the monomiality principle are given. Finally, graphical representations are presented to illustrate the behavior and potential applications of the three-variable q-truncated exponential Gould–Hopper-based Appell polynomials. Full article

(This article belongs to the Special Issue Polynomials: Theory and Applications, 2nd Edition)

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20 pages, 1906 KiB

Open AccessFeature PaperArticle

Creating Tail Dependence by Rough Stochastic Correlation Satisfying a Fractional SDE; An Application in Finance

by László Márkus, Ashish Kumar and Amina Darougi

Mathematics 2025, 13(13), 2072; https://doi.org/10.3390/math13132072 - 23 Jun 2025

Abstract

The stochastic correlation for Brownian motions is the integrand in the formula of their quadratic covariation. The estimation of this stochastic process becomes available from the temporally localized correlation of latent price driving Brownian motions in stochastic volatility models for asset prices. By [...] Read more.

The stochastic correlation for Brownian motions is the integrand in the formula of their quadratic covariation. The estimation of this stochastic process becomes available from the temporally localized correlation of latent price driving Brownian motions in stochastic volatility models for asset prices. By analyzing this process for Apple and Microsoft stock prices traded minute-wise, we give statistical evidence for the roughness of its paths. Moment scaling indicates fractal behavior, and both fractal dimensions (approx. 1.95) and Hurst exponent estimates (around 0.05) point to rough paths. We model this rough stochastic correlation by a suitably transformed fractional Ornstein–Uhlenbeck process and simulate artificial stock prices, which allows computing tail dependence and the Herding Behavior Index (HIX) as functions in time. The computed HIX is hardly variable in time (e.g., standard deviation of 0.003–0.006); on the contrary, tail dependence fluctuates more heavily (e.g., standard deviation approx. 0.04). This results in a higher correlation risk, i.e., more frequent sudden coincident appearance of extreme prices than a steady HIX value indicates. Full article

(This article belongs to the Special Issue Modeling Multivariate Financial Time Series and Computing)

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18 pages, 3277 KiB

Open AccessArticle

Neural Networks in the Delayed Teleoperation of a Skid-Steering Robot

by Kleber Patiño, Emanuel Slawiñski, Marco Moran-Armenta, Vicente Mut, Francisco G. Rossomando and Javier Moreno-Valenzuela

Mathematics 2025, 13(13), 2071; https://doi.org/10.3390/math13132071 - 23 Jun 2025

Abstract

Bilateral teleoperation of skid-steering mobile robots with time-varying delays presents significant challenges in ensuring accurate leader–follower coupling. This article presents a novel controller for a bilateral teleoperation system composed of a robot manipulator and a skid-steering mobile robot. The proposed controller leverages neural [...] Read more.

Bilateral teleoperation of skid-steering mobile robots with time-varying delays presents significant challenges in ensuring accurate leader–follower coupling. This article presents a novel controller for a bilateral teleoperation system composed of a robot manipulator and a skid-steering mobile robot. The proposed controller leverages neural networks to compensate for ground–robot interactions, uncertain dynamics, and communication delays. The control strategy integrates a shared scheme between damping injection and two neural networks, enhancing the robustness and adaptability of the delayed system. A rigorous theoretical analysis of the closed-loop teleoperation system is provided, establishing conditions of control parameters to ensure stability and convergence of the coordination errors. The proposed method is validated through numerical testing, demonstrating strong agreement between theoretical outcomes and simulation results. Full article

(This article belongs to the Special Issue Advanced Control Theory in Robot System)

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27 pages, 3082 KiB

Open AccessArticle

Analyzing Systemic Risk Spillover Networks Through a Time-Frequency Approach

by Liping Zheng, Ziwei Liang, Jiaoting Yi and Yuhan Zhu

Mathematics 2025, 13(13), 2070; https://doi.org/10.3390/math13132070 - 22 Jun 2025

Viewed by 22

Abstract

This paper investigates the spillover effects and transmission networks of systemic risk within China’s national economic sectors under extreme conditions from both time and frequency domain perspectives, building upon the spillover index methodology and calculating the ∆CoVaR index for Chinese industries. The findings [...] Read more.

This paper investigates the spillover effects and transmission networks of systemic risk within China’s national economic sectors under extreme conditions from both time and frequency domain perspectives, building upon the spillover index methodology and calculating the ∆CoVaR index for Chinese industries. The findings indicate the following: (1) Extreme-risk spillovers synchronize across industries but exhibit pronounced time-varying peaks during the 2008 Global Financial Crisis, the 2015 crash, and the COVID-19 pandemic. (2) Long-term spillovers dominate overall connectedness, highlighting the lasting impact of fundamentals and structural linkages. (3) In terms of risk volatility, Energy, Materials, Consumer Discretionary, and Financials are most sensitive to systemic market shocks. (4) On the risk spillover effect, Consumer Discretionary, Industrials, Healthcare, and Information Technology consistently act as net transmitters of extreme risk, while Energy, Materials, Consumer Staples, Financials, Telecom Services, Utilities, and Real Estate primarily serve as net receivers. Based on these findings, the paper suggests deepening the regulatory mechanisms for systemic risk, strengthening the synergistic effect of systemic risk measurement and early warning indicators, and coordinating risk monitoring, early warning, and risk prevention and mitigation. It further emphasizes the importance of avoiding fragmented regulation by establishing a joint risk prevention mechanism across sectors and departments, strengthening the supervision of inter-industry capital flows. Finally, it highlights the need to closely monitor the formation mechanisms and transmission paths of new financial risks under the influence of the pandemic to prevent the accumulation and eruption of risks in the post-pandemic era. Authorities must conduct annual “Industry Transmission Reviews” to map emerging risk nodes and supply-chain vulnerabilities, refine policy tools, and stabilize market expectations so as to forestall the build-up and sudden release of new systemic shocks. Full article

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27 pages, 458 KiB

Open AccessArticle

Optimal Control of an Eco-Epidemiological Reaction-Diffusion Model

by Runmei Du, Xinghua Liang, Yang Na and Fengdan Xu

Mathematics 2025, 13(13), 2069; https://doi.org/10.3390/math13132069 - 22 Jun 2025

Viewed by 14

Abstract

In this paper, a prey–predator diffusion model with isolation and drug treatment control measures for prey infection is studied. The main objective is to find an optimal control that minimizes the population density of infected prey and the costs of isolation and drug [...] Read more.

In this paper, a prey–predator diffusion model with isolation and drug treatment control measures for prey infection is studied. The main objective is to find an optimal control that minimizes the population density of infected prey and the costs of isolation and drug treatment for infected prey. Through analysis, the existence and uniqueness of weak solution, as well as the existence and local uniqueness of optimal controls are proven. The first-order necessary condition is derived, and the feasibility of the theoretical proof is verified through numerical simulations. Full article

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44 pages, 3458 KiB

Open AccessArticle

Fractional Optimizers for LSTM Networks in Financial Time Series Forecasting

by Mustapha Ez-zaiym, Yassine Senhaji, Meriem Rachid, Karim El Moutaouakil and Vasile Palade

Mathematics 2025, 13(13), 2068; https://doi.org/10.3390/math13132068 - 22 Jun 2025

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Abstract

This study investigates the theoretical foundations and practical advantages of fractional-order optimization in computational machine learning, with a particular focus on stock price forecasting using long short-term memory (LSTM) networks. We extend several widely used optimization algorithms—including Adam, RMSprop, SGD, Adadelta, FTRL, Adamax, [...] Read more.

This study investigates the theoretical foundations and practical advantages of fractional-order optimization in computational machine learning, with a particular focus on stock price forecasting using long short-term memory (LSTM) networks. We extend several widely used optimization algorithms—including Adam, RMSprop, SGD, Adadelta, FTRL, Adamax, and Adagrad—by incorporating fractional derivatives into their update rules. This novel approach leverages the memory-retentive properties of fractional calculus to improve convergence behavior and model efficiency. Our experimental analysis evaluates the performance of fractional-order optimizers on LSTM networks tasked with forecasting stock prices for major companies such as AAPL, MSFT, GOOGL, AMZN, META, NVDA, JPM, V, and UNH. Considering four metrics (Sharpe ratio, directional accuracy, cumulative return, and MSE), the results show that fractional orders can significantly enhance prediction accuracy for moderately volatile stocks, especially among lower-cap assets. However, for highly volatile stocks, performance tends to degrade with higher fractional orders, leading to erratic and inconsistent forecasts. In addition, fractional optimizers with short-memory truncation offer a favorable trade-off between computational efficiency and modeling accuracy in medium-frequency financial applications. Their enhanced capacity to capture long-range dependencies and robust performance in noisy environments further justify their adoption in such contexts. These results suggest that fractional-order optimization holds significant promise for improving financial forecasting models—provided that the fractional parameters are carefully tuned to balance memory effects with system stability. Full article

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25 pages, 3475 KiB

Open AccessFeature PaperArticle

Rényi Entropy-Based Shrinkage with RANSAC Refinement for Sparse Time-Frequency Distribution Reconstruction

by Vedran Jurdana

Mathematics 2025, 13(13), 2067; https://doi.org/10.3390/math13132067 - 22 Jun 2025

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Abstract

Compressive sensing in the ambiguity domain facilitates high-performance reconstruction of time-frequency distributions (TFDs) for non-stationary signals. However, identifying the optimal regularization parameter in the absence of prior knowledge remains a significant challenge. The Rényi entropy-based two-step iterative shrinkage/thresholding (RTwIST) algorithm addresses this issue [...] Read more.

Compressive sensing in the ambiguity domain facilitates high-performance reconstruction of time-frequency distributions (TFDs) for non-stationary signals. However, identifying the optimal regularization parameter in the absence of prior knowledge remains a significant challenge. The Rényi entropy-based two-step iterative shrinkage/thresholding (RTwIST) algorithm addresses this issue by incorporating local component estimates to guide adaptive thresholding, thereby improving interpretability and robustness. Nevertheless, RTwIST may struggle to accurately isolate components in cases of significant amplitude variations or component intersections. In this work, an enhanced RTwIST framework is proposed, integrating the random sample consensus (RANSAC)-based refinement stage that iteratively extracts individual components and fits smooth trajectories to their peaks. The best-fitting curves are selected by minimizing a dedicated objective function that balances amplitude consistency and trajectory smoothness. Experimental validation on both synthetic and real-world electroencephalogram (EEG) signals demonstrates that the proposed method achieves superior reconstruction accuracy, enhanced auto-term continuity, and improved robustness compared to the original RTwIST and several state-of-the-art algorithms. Full article

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11 pages, 257 KiB

Open AccessArticle

Quasi-Irreducibility of Nonnegative Biquadratic Tensors

by Liqun Qi, Chunfeng Cui and Yi Xu

Mathematics 2025, 13(13), 2066; https://doi.org/10.3390/math13132066 - 22 Jun 2025

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Abstract

While the adjacency tensor of a bipartite 2-graph is a nonnegative biquadratic tensor, it is inherently reducible. To address this limitation, we introduce the concept of quasi-irreducibility in this paper. The adjacency tensor of a bipartite 2-graph is quasi-irreducible if that bipartite 2-graph [...] Read more.

While the adjacency tensor of a bipartite 2-graph is a nonnegative biquadratic tensor, it is inherently reducible. To address this limitation, we introduce the concept of quasi-irreducibility in this paper. The adjacency tensor of a bipartite 2-graph is quasi-irreducible if that bipartite 2-graph is not bi-separable. This new concept reveals important spectral properties: although all M⁺-eigenvalues are M⁺⁺-eigenvalues for irreducible nonnegative biquadratic tensors, the M⁺-eigenvalues of a quasi-irreducible nonnegative biquadratic tensor can be either M⁰-eigenvalues or M⁺⁺-eigenvalues. Furthermore, we establish a max-min theorem for the M-spectral radius of a nonnegative biquadratic tensor. Full article

(This article belongs to the Special Issue Spectral Theory of Tensors, Tensor (Rank) Decompositions, and Their Applications)

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18 pages, 931 KiB

Open AccessArticle

Slip-Driven Interaction of Dual Spheres in Couple Stress Fluids Within a Permeable Medium

by Shreen El-Sapa and Munirah Aali Alotaibi

Mathematics 2025, 13(13), 2065; https://doi.org/10.3390/math13132065 - 21 Jun 2025

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Abstract

This study investigates the consistent and uniform movement of two spherical particles within an infinite porous medium saturated with a couple stress fluid, with a particular focus on the effects of surface slippage. The research reveals that surface slippage significantly reduces the drag [...] Read more.

This study investigates the consistent and uniform movement of two spherical particles within an infinite porous medium saturated with a couple stress fluid, with a particular focus on the effects of surface slippage. The research reveals that surface slippage significantly reduces the drag force experienced by the particles, thereby influencing their hydrodynamic interactions. Conversely, increases in permeability and particle size similarity tend to enhance both the drag force and the inter-particle interaction forces, affecting the overall dynamics of particle motion. The analysis is conducted within the low-Reynolds-number regime, characteristic of laminar flow dominated by viscous forces, and employs boundary collocation methodologies to derive semi-analytical solutions to the governing differential equations. This approach enables a detailed characterization of the flow behavior and inter-particle forces in intricate fluid environments, including those with porous matrices and complex rheological properties. The findings from this investigation are consistent with prior numerical analyses, notably those conducted by Alotaibi and El-Sapa (2025), and corroborate earlier studies by Shehadeh and Ashmawy (2019), which examined cases of no slippage and permeability effects. Additionally, the results align with earlier research by Shreen et al. (2018) concerning viscous fluids, thereby reinforcing the validity of the conclusions. Overall, the study enhances the understanding of particle-fluid interactions in porous, couple stress-rich media, providing valuable insights into the roles of surface slippage, permeability, and particle size in determining hydrodynamic forces. Full article

(This article belongs to the Section E: Applied Mathematics)

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20 pages, 732 KiB

Open AccessFeature PaperArticle

On Minimizing Influences Under Multi-Attribute Models

by Bo-Yao Wang

Mathematics 2025, 13(13), 2064; https://doi.org/10.3390/math13132064 - 21 Jun 2025

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Abstract

In classical transferable-utility models, components typically participate in an all-or-nothing manner and are evaluated under a single criterion. This study generalizes such models by allowing each component to engage through multiple acting measures and by incorporating multiple evaluating attributes simultaneously. We introduce two [...] Read more.

In classical transferable-utility models, components typically participate in an all-or-nothing manner and are evaluated under a single criterion. This study generalizes such models by allowing each component to engage through multiple acting measures and by incorporating multiple evaluating attributes simultaneously. We introduce two influence-based assessments, the stable min value and the minimal self-stable value, to evaluate fair assessments of minimal impact across multi-attribute multi-choice environments. These values are rigorously defined via axiomatic characterizations grounded in minimal influence behavior, where coalitions select activity levels that jointly minimize systemic effects. A key theoretical contribution is the identification of a unique, 0-normalized, and efficient multi-attribute potential function corresponding to the minimal self-stable value. The proposed framework enables structured and interpretable evaluation of influence in complex cooperative systems with heterogeneous participation and conflicting objectives. Full article

(This article belongs to the Special Issue Advances in Mathematical Optimization in Operational Research)

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15 pages, 355 KiB

Open AccessArticle

A UAV-Assisted STAR-RIS Network with a NOMA System

by Jiyin Lan, Yuyang Peng, Mohammad Meraj Mirza and Fawaz AL-Hazemi

Mathematics 2025, 13(13), 2063; https://doi.org/10.3390/math13132063 - 21 Jun 2025

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Abstract

In this paper, we investigate a simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-assisted non-orthogonal multiple access (NOMA) communication system where the STAR-RIS is mounted on an unmanned aerial vehicle (UAV) with adjustable altitude. Due to severe blockages in urban environments, direct links [...] Read more.

In this paper, we investigate a simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-assisted non-orthogonal multiple access (NOMA) communication system where the STAR-RIS is mounted on an unmanned aerial vehicle (UAV) with adjustable altitude. Due to severe blockages in urban environments, direct links from the base station (BS) to users are assumed unavailable, and signal transmission is realized via the STAR-RIS. We formulate a joint optimization problem that maximizes the system sum rate by jointly optimizing the UAV’s altitude, BS beamforming vectors, and the STAR-RIS phase shifts, while considering Rician fading channels with altitude-dependent Rician factors. To tackle the maximum achievable rate problem, we adopt a block-wise optimization framework and employ semidefinite relaxation and gradient descent methods. Simulation results show that the proposed scheme achieves up to 22% improvement in achievable rate and significant reduction in bit error rate (BER) compared to benchmark schemes, demonstrating its effectiveness in integrating STAR-RIS and UAV in NOMA networks. Full article

(This article belongs to the Special Issue Mathematical Modelling for Cooperative Communications)

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25 pages, 528 KiB

Open AccessFeature PaperArticle

Lightweight and Security-Enhanced Key Agreement Protocol Using PUF for IoD Environments

by Sangjun Lee, Seunghwan Son and Youngho Park

Mathematics 2025, 13(13), 2062; https://doi.org/10.3390/math13132062 - 21 Jun 2025

Viewed by 84

Abstract

With the increasing demand for drones in diverse tasks, the Internet of Drones (IoD) has recently emerged as a significant technology in academia and industry. The IoD environment enables various services, such as traffic and environmental monitoring, disaster situation management, and military operations. [...] Read more.

With the increasing demand for drones in diverse tasks, the Internet of Drones (IoD) has recently emerged as a significant technology in academia and industry. The IoD environment enables various services, such as traffic and environmental monitoring, disaster situation management, and military operations. However, IoD communication is vulnerable to security threats due to the exchange of sensitive information over insecure public channels. Moreover, public key-based cryptographic schemes are impractical for communication with resource-constrained drones due to their limited computational capability and resource capacity. Therefore, a secure and lightweight key agreement scheme must be developed while considering the characteristics of the IoD environment. In 2024, Alzahrani proposed a secure key agreement protocol for securing the IoD environment. However, Alzahrani’s protocol suffers from high computational overhead due to its reliance on elliptic curve cryptography and is vulnerable to drone and mobile user impersonation attacks and session key disclosure attacks by eavesdropping on public-channel messages. Therefore, this work proposes a lightweight and security-enhanced key agreement scheme for the IoD environment to address the limitations of Alzahrani’s protocol. The proposed protocol employs a physical unclonable function and simple cryptographic operations (XOR and hash functions) to achieve high security and efficiency. This work demonstrates the security of the proposed protocol using informal security analysis. This work also conducted formal security analysis using the Real-or-Random (RoR) model, Burrows–Abadi–Needham (BAN) logic, and Automated Verification of Internet Security Protocols and Applications (AVISPA) simulation to verify the proposed protocol’s session key security, mutual authentication ability, and resistance to replay and MITM attacks, respectively. Furthermore, this work demonstrates that the proposed protocol offers better performance and security by comparing the computational and communication costs and security features with those of relevant protocols. Full article

(This article belongs to the Special Issue Advanced Research on Information System Security and Privacy, 2nd Edition)

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37 pages, 6550 KiB

Open AccessArticle

Multiphase Transport Network Optimization: Mathematical Framework Integrating Resilience Quantification and Dynamic Algorithm Coupling

by Linghao Ren, Xinyue Li, Renjie Song, Yuning Wang, Meiyun Gui and Bo Tang

Mathematics 2025, 13(13), 2061; https://doi.org/10.3390/math13132061 - 21 Jun 2025

Viewed by 47

Abstract

This study proposes a multi-dimensional urban transportation network optimization framework (MTNO-RQDC) to address structural failure risks from aging infrastructure and regional connectivity bottlenecks. Through dual-dataset validation using both the Baltimore road network and PeMS07 traffic flow data, we first develop a traffic simulation [...] Read more.

This study proposes a multi-dimensional urban transportation network optimization framework (MTNO-RQDC) to address structural failure risks from aging infrastructure and regional connectivity bottlenecks. Through dual-dataset validation using both the Baltimore road network and PeMS07 traffic flow data, we first develop a traffic simulation model integrating Dijkstra’s algorithm with capacity-constrained allocation strategies for guiding reconstruction planning for the collapsed Francis Scott Key Bridge. Next, we create a dynamic adaptive public transit optimization model using an entropy weight-TOPSIS decision framework coupled with an improved simulated annealing algorithm (ISA-TS), achieving coordinated suburban–urban network optimization while maintaining 92.3% solution stability under simulated node failure conditions. The framework introduces three key innovations: (1) a dual-layer regional division model combining K-means geographical partitioning with spectral clustering functional zoning; (2) fault-tolerant network topology optimization demonstrated through 1000-epoch Monte Carlo failure simulations; (3) cross-dataset transferability validation showing 15.7% performance variance between Baltimore and PeMS07 environments. Experimental results demonstrate a 28.7% reduction in road network traffic variance (from 42,760 to 32,100), 22.4% improvement in public transit path redundancy, and 30.4–44.6% decrease in regional traffic load variance with minimal costs. Hyperparameter analysis reveals two optimal operational modes: rapid cooling (rate = 0.90) achieves 85% improvement within 50 epochs for emergency response, while slow cooling (rate = 0.99) yields 12.7% superior solutions for long-term planning. The framework establishes a new multi-objective paradigm balancing structural resilience, functional connectivity, and computational robustness for sustainable smart city transportation systems. Full article

(This article belongs to the Special Issue Mathematical Methods and Models in Information Security with Applications)

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24 pages, 1096 KiB

Open AccessFeature PaperArticle

Improved Test for High-Dimensional Mean Vectors and Covariance Matrices Using Random Projection

by Tung-Lung Wu

Mathematics 2025, 13(13), 2060; https://doi.org/10.3390/math13132060 - 21 Jun 2025

Viewed by 43

Abstract

This paper proposes an improved random projection-based method for testing high-dimensional two-sample mean vectors and covariance matrices. For mean testing, the proposed approach incorporates training data to guide the construction of projection matrices toward the estimated mean difference, thereby substantially enhancing the power [...] Read more.

This paper proposes an improved random projection-based method for testing high-dimensional two-sample mean vectors and covariance matrices. For mean testing, the proposed approach incorporates training data to guide the construction of projection matrices toward the estimated mean difference, thereby substantially enhancing the power of the projected Hotelling’s

T^{2}

statistic. We introduce three aggregation strategies—maximum, average, and percentile-based—to ensure stable performance across multiple projections. For covariance testing, the method employs data-driven projections aligned with the leading eigenvector of the sample covariance matrix to amplify the differences between matrices. Aggregation strategies—maximum-, average-, and percentile-based for the mean problem and minimum and average p-values for the covariance problem—are developed to further stabilize performance across repeated projections. An application to gene expression data is provided to illustrate the method. Extensive simulation studies show that the proposed method performs favorably compared to a recent state-of-the-art technique, particularly in detecting sparse signals, while maintaining control of the Type-I error rate. Full article

(This article belongs to the Special Issue Computational Intelligence in Addressing Data Heterogeneity)

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20 pages, 992 KiB

Open AccessFeature PaperReview

Markov-Chain Perturbation and Approximation Bounds in Stochastic Biochemical Kinetics

by Alexander Y. Mitrophanov

Mathematics 2025, 13(13), 2059; https://doi.org/10.3390/math13132059 - 21 Jun 2025

Viewed by 58

Abstract

Markov chain perturbation theory is a rapidly developing subfield of the theory of stochastic processes. This review outlines emerging applications of this theory in the analysis of stochastic models of chemical reactions, with a particular focus on biochemistry and molecular biology. We begin [...] Read more.

Markov chain perturbation theory is a rapidly developing subfield of the theory of stochastic processes. This review outlines emerging applications of this theory in the analysis of stochastic models of chemical reactions, with a particular focus on biochemistry and molecular biology. We begin by discussing the general problem of approximate modeling in stochastic chemical kinetics. We then briefly review some essential mathematical results pertaining to perturbation bounds for continuous-time Markov chains, emphasizing the relationship between robustness under perturbations and the rate of exponential convergence to the stationary distribution. We illustrate the use of these results to analyze stochastic models of biochemical reactions by providing concrete examples. Particular attention is given to fundamental problems related to approximation accuracy in model reduction. These include the partial thermodynamic limit, the irreversible-reaction limit, parametric uncertainty analysis, and model reduction for linear reaction networks. We conclude by discussing generalizations and future developments of these methodologies, such as the need for time-inhomogeneous Markov models. Full article

(This article belongs to the Section D1: Probability and Statistics)

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18 pages, 791 KiB

Open AccessFeature PaperArticle

Gaussian Process with Vine Copula-Based Context Modeling for Contextual Multi-Armed Bandits

by Jong-Min Kim

Mathematics 2025, 13(13), 2058; https://doi.org/10.3390/math13132058 - 21 Jun 2025

Viewed by 84

Abstract

We propose a novel contextual multi-armed bandit (CMAB) framework that integrates copula-based context generation with Gaussian Process (GP) regression for reward modeling, addressing complex dependency structures and uncertainty in sequential decision-making. Context vectors are generated using Gaussian and vine copulas to capture nonlinear [...] Read more.

We propose a novel contextual multi-armed bandit (CMAB) framework that integrates copula-based context generation with Gaussian Process (GP) regression for reward modeling, addressing complex dependency structures and uncertainty in sequential decision-making. Context vectors are generated using Gaussian and vine copulas to capture nonlinear dependencies, while arm-specific reward functions are modeled via GP regression with Beta-distributed targets. We evaluate three widely used bandit policies—Thompson Sampling (TS),

ε

-Greedy, and Upper Confidence Bound (UCB)—on simulated environments informed by real-world datasets, including Boston Housing and Wine Quality. The Boston Housing dataset exemplifies heterogeneous decision boundaries relevant to housing-related marketing, while the Wine Quality dataset introduces sensory feature-based arm differentiation. Our empirical results indicate that the

ε

-Greedy policy consistently achieves the highest cumulative reward and lowest regret across multiple runs, outperforming both GP-based TS and UCB in high-dimensional, copula-structured contexts. These findings suggest that combining copula theory with GP modeling provides a robust and flexible foundation for data-driven sequential experimentation in domains characterized by complex contextual dependencies. Full article

(This article belongs to the Special Issue Uncertainty Quantification Techniques in Statistics, Machine Learning and FinTech: 2nd Edition)

22 pages, 1233 KiB

Open AccessArticle

Radio Mean Labeling Algorithm, Its Complexity and Existence Results

by Meera Saraswathi, K. N. Meera and Yuqing Lin

Mathematics 2025, 13(13), 2057; https://doi.org/10.3390/math13132057 - 20 Jun 2025

Viewed by 86

Abstract

Radio mean labeling of a connected graph G is an assignment of distinct positive integers to the vertices of G satisfying a mathematical constraint called radio mean condition. The maximum label assigned to any vertex of G is called the [...] Read more.

Radio mean labeling of a connected graph G is an assignment of distinct positive integers to the vertices of G satisfying a mathematical constraint called radio mean condition. The maximum label assigned to any vertex of G is called the

s p a n

of the radio mean labeling. The minimum

s p a n

of all feasible radio mean labelings of G is the radio mean number of G, denoted by

r m n (G)

. In our previous study, we proved that if G has order n, then

r m n (G) \in [n, r m n (P_{n})]

where

P_{n}

is a path of order n. All graphs of diameters 1, 2 and 3 have the radio mean number equal to order n. However, they are not the only graphs on n vertices with radio mean number n. Graphs isomorphic to path

P_{n}

are the graphs having the maximum diameter among the set of all graphs of order n and they possess the maximum feasible radio mean number. In this paper, we show that, for any integer in the range of achievable radio mean numbers, there always exists a graph of order n with the given integer as its radio mean number. This is approached by introducing a special type of tree whose construction is detailed in the article. The task of assigning radio mean labels to a graph can be considered as an optimization problem. This paper critiques the limitations of existing Integer Linear Programming (ILP) models for assigning radio mean labeling to graphs and proposes a new ILP model. The existing ILP model does not guarantee that the vertex labels are distinct, positive and satisfy the radio mean condition, prompting the need for an improved approach. We propose a new ILP model which involves

n^{2}

constraints is the input graph’s order is n. We obtain a radio mean labeling of cycle of order 10 using the new ILP. In our previous study, we showed that, for any graph G, we can extend the radio mean labelings of its diametral paths to the vertex set of G and obtain radio mean labelings of G. This insight forms the basis for an algorithm presented in this paper to obtain radio mean labels for a given graph G with n vertices and diameter d. The correctness and complexity of this algorithm are analyzed in detail. Radio mean labelings have been proposed for cryptographic key generation in previous works, and the algorithm presented in this paper is general enough to support similar applications across various graph structures. Full article

(This article belongs to the Section E1: Mathematics and Computer Science)

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23 pages, 807 KiB

Open AccessArticle

On the Limiting Distribution of the Spectra of Random Block Matrices

by Alexander N. Tikhomirov

Mathematics 2025, 13(13), 2056; https://doi.org/10.3390/math13132056 - 20 Jun 2025

Viewed by 71

Abstract

The behavior of the spectra of symmetric block-type random matrices with symmetric blocks of high dimensionality is considered in this paper. Under minimal conditions regarding the distributions of matrix block elements (Lindeberg conditions), the universality of the limiting empirical distribution function of block-type [...] Read more.

The behavior of the spectra of symmetric block-type random matrices with symmetric blocks of high dimensionality is considered in this paper. Under minimal conditions regarding the distributions of matrix block elements (Lindeberg conditions), the universality of the limiting empirical distribution function of block-type random matrices is shown. Full article

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25 pages, 356 KiB

Open AccessArticle

Nonlocal Nonlinear Fractional-Order Sequential Hilfer–Caputo Multivalued Boundary-Value Problems

by Sotiris K. Ntouyas, Bashir Ahmad and Jessada Tariboon

Mathematics 2025, 13(13), 2055; https://doi.org/10.3390/math13132055 - 20 Jun 2025

Viewed by 95

Abstract

This paper is concerned with the investigation of a nonlocal sequential multistrip boundary-value problem for fractional differential inclusions, involving

(k_{1}, ψ_{1})

-Hilfer and

(k_{2}, ψ_{2})

-Caputo fractional derivative operators, and [...] Read more.

This paper is concerned with the investigation of a nonlocal sequential multistrip boundary-value problem for fractional differential inclusions, involving

(k_{1}, ψ_{1})

-Hilfer and

(k_{2}, ψ_{2})

-Caputo fractional derivative operators, and

(k_{2}, ψ_{2})

- Riemann–Liouville fractional integral operators. The problem considered in the present study is of a more general nature as the

(k_{1}, ψ_{1})

-Hilfer fractional derivative operator specializes to several other fractional derivative operators by fixing the values of the function

ψ_{1}

and the parameter

β

. Also the

(k_{2}, ψ_{2})

-Riemann–Liouville fractional integral operator appearing in the multistrip boundary conditions is a generalized form of the

ψ_{2}

-Riemann–Liouville,

k_{2}

-Riemann–Liouville, and the usual Riemann–Liouville fractional integral operators (see the details in the paragraph after the formulation of the problem. Our study includes both convex and non-convex valued maps. In the upper semicontinuous case, we prove four existence results with the aid of the Leray–Schauder nonlinear alternative for multivalued maps, Mertelli’s fixed-point theorem, the nonlinear alternative for contractive maps, and Krasnoselskii’s multivalued fixed-point theorem when the multivalued map is convex-valued and

L^{1}

-Carathéodory. The lower semicontinuous case is discussed by making use of the nonlinear alternative of the Leray–Schauder type for single-valued maps together with Bressan and Colombo’s selection theorem for lower semicontinuous maps with decomposable values. Our final result for the Lipschitz case relies on the Covitz–Nadler fixed-point theorem for contractive multivalued maps. Examples are offered for illustrating the results presented in this study. Full article

(This article belongs to the Special Issue Recent Investigations of Differential and Fractional Equations and Inclusions, 3rd Edition)

26 pages, 2686 KiB

Open AccessFeature PaperArticle

Quantum Entanglement Between Charge Qubit and Mechanical Cat-States in Nanoelectromechanical System

by Matija Tečer and Danko Radić

Mathematics 2025, 13(13), 2054; https://doi.org/10.3390/math13132054 - 20 Jun 2025

Viewed by 75

Abstract

We present a detailed mathematical description, both an analytical model and a numerical simulation, of a physical system based on a superconducting nanoelectromechanical setup that generates nanomechanical cat-states entangled with charge qubit states. The system consists of a superconducting grain in a regime [...] Read more.

We present a detailed mathematical description, both an analytical model and a numerical simulation, of a physical system based on a superconducting nanoelectromechanical setup that generates nanomechanical cat-states entangled with charge qubit states. The system consists of a superconducting grain in a regime of the Cooper pair box (the charge qubit) that performs mechanical vibrations between two bulk superconductors. Operation of the device is based on the AC Josephson effect, i.e., the phase difference between superconducting electrodes is controlled by a DC bias voltage following the operational switch on/off protocol. We compare an analytical idealised solution with numerical simulation using experimentally feasible parameters, different decoherence processes, as well as imperfections of experimental procedures such as time-control of the bias voltage, to get insight into how they influence the time-evolution of the realistic system, deteriorate the quantum coherence, and affect the formation of the cat-states. Full article

(This article belongs to the Section E: Applied Mathematics)

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Mathematics, Volume 13, Issue 13 (July-1 2025) – 45 articles

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