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Search Results (602)

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37 pages, 45288 KiB  
Article
Dynamic Analysis and Application of 6D Multistable Memristive Chaotic System with Wide Range of Hyperchaotic States
by Fei Yu, Yumba Musoya Gracia, Rongyao Guo, Zhijie Ying, Jiarong Xu, Wei Yao, Jie Jin and Hairong Lin
Axioms 2025, 14(8), 638; https://doi.org/10.3390/axioms14080638 - 15 Aug 2025
Abstract
In this study, we present a novel, six-dimensional, multistable, memristive, hyperchaotic system model demonstrating two positive Lyapunov exponents. With the maximum Lyapunov exponents surpassing 21, the developed system shows pronounced hyperchaotic behavior. The dynamical behavior was analyzed through phase portraits, bifurcation diagrams, and [...] Read more.
In this study, we present a novel, six-dimensional, multistable, memristive, hyperchaotic system model demonstrating two positive Lyapunov exponents. With the maximum Lyapunov exponents surpassing 21, the developed system shows pronounced hyperchaotic behavior. The dynamical behavior was analyzed through phase portraits, bifurcation diagrams, and Lyapunov exponent spectra. Parameter b was a key factor in regulating the dynamical behavior of the system, mainly affecting the strength and direction of the influence of z1 on z2. It was found that when the system parameter b was within a wide range of [13,300], the system remained hyperchaotic throughout. Analytical establishment of multistability mechanisms was achieved through invariance analysis of the state variables under specific coordinate transformations. Furthermore, offset boosting control was realized by strategically modulating the fifth state variable, z5. The FPGA-based experimental results demonstrated that attractors observed via an oscilloscope were in close agreement with numerical simulations. To validate the system’s reliability for cybersecurity applications, we designed a novel image encryption method utilizing this hyperchaotic model. The information entropy of the proposed encryption algorithm was closer to the theoretical maximum value of 8. This indicated that the system can effectively disrupt statistical patterns. Experimental outcomes confirmed that the proposed image encryption method based on the hyperchaotic system exhibits both efficiency and reliability. Full article
(This article belongs to the Special Issue Nonlinear Dynamical System and Its Applications)
13 pages, 885 KiB  
Article
The G-allele of rs10830963 in MTNR1B Exerts Stage-Specific Effects Across the Trajectory of Type 2 Diabetes: A Multi-State Analysis
by Yao Huang, Xiuping Dou, Man He, Yang Su, Hualiang Lin and Yin Yang
Int. J. Mol. Sci. 2025, 26(16), 7855; https://doi.org/10.3390/ijms26167855 - 14 Aug 2025
Abstract
Although the MTNR1B single nucleotide polymorphism rs10830963 has been strongly associated with the onset of type 2 diabetes (T2D), its association with the progression and prognosis of T2D has been understudied. We conducted this prospective analysis based on the UK Biobank cohort study. [...] Read more.
Although the MTNR1B single nucleotide polymorphism rs10830963 has been strongly associated with the onset of type 2 diabetes (T2D), its association with the progression and prognosis of T2D has been understudied. We conducted this prospective analysis based on the UK Biobank cohort study. Microvascular complications (MIC) of T2D in this study included diabetic retinopathy, diabetic neuropathy, and diabetic kidney disease. Macrovascular complications (MAC) of T2D included diabetic coronary artery disease, diabetic cerebrovascular disease, and diabetic peripheral vascular disease. The multi-state model was used to analyze the association between the polymorphism of rs10830963 and the trajectory of T2D. The accelerated failure time (AFT) model was used to assess the association between rs10830963 and the onset of T2D and T2D comorbidities. A total of 283,531 middle- and old-age participants were included. During a median follow-up of 13.7 years, 11,947 participants developed T2D, 1556 participants developed MIC, 1797 participants developed MAC, and 618 participants died. In the additive model, the G risk allele of rs10830963 was significantly associated with an increased risk of the transition from T2D-free to T2D (HR = 1.050, 95% CI: 1.020, 1.079) and a decreased risk of the transition from T2D to MIC (HR = 0.918, 95% CI: 0.850, 0.992), particularly from T2D to diabetic retinopathy (HR = 0.882, 95% CI: 0.782, 0.995). Besides, the G risk allele of rs10830963 accelerated the transition from T2D-free to T2D (Time Ratio [TR] = 0.966, 95% CI: 0.947, 0.986) and slowed down the transition from T2D to MIC (TR = 1.067, 95% CI: 1.030, 1.105). The MTNR1B single nucleotide polymorphism rs10830963 was associated with an increased risk of T2D and a decreased risk of MIC, particularly diabetic retinopathy among T2D individuals. Our results highlight that rs10830963 might play differential roles in the onset and progression of T2D. Full article
(This article belongs to the Section Molecular Genetics and Genomics)
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1 pages, 115 KiB  
Retraction
RETRACTED: He et al. The Multi-Station Fusion-Based Radiation Source Localization Method Based on Spectrum Energy. Sensors 2025, 25, 1339
by Guojin He, Yulong Hao and Yaocong Xie
Sensors 2025, 25(16), 4976; https://doi.org/10.3390/s25164976 - 12 Aug 2025
Viewed by 114
Abstract
The journal Sensors retracts the article titled “The Multi-Station Fusion-Based Radiation Source Localization Method Based on Spectrum Energy” [...] Full article
18 pages, 8218 KiB  
Article
Seasonal Circulation Characteristics of Oceanic System in the Beibu Gulf Based on Observations and Numerical Simulations
by Gongpeng Liu, Na Zhang, Yuping Yang and Chenghao Wang
Water 2025, 17(16), 2365; https://doi.org/10.3390/w17162365 - 9 Aug 2025
Viewed by 205
Abstract
The Beibu Gulf’s ocean circulation system regulates regional marine ecosystems, sediment transport, and coastal geomorphology while also supporting vital economic activities. This study integrates one-year current observations from four in-situ current observation stations (B1−B4) with simulations using the Regional Ocean Modeling System (ROMS) [...] Read more.
The Beibu Gulf’s ocean circulation system regulates regional marine ecosystems, sediment transport, and coastal geomorphology while also supporting vital economic activities. This study integrates one-year current observations from four in-situ current observation stations (B1−B4) with simulations using the Regional Ocean Modeling System (ROMS) to characterize circulation dynamics in the gulf. Observations show persistent northward subtidal currents west of Hainan Island year-round, primarily sustained by tidal-induced residual currents. These currents briefly reverse southward during strong northerly wind events, whereas subtidal currents in the northern Beibu Gulf are more wind-dependent, showing pronounced seasonal variations. Numerical results confirm that winter circulation is dominated by a basin-wide cyclonic gyre driven by northeasterly monsoons. In summer, circulation in the northern gulf is cyclonic under southeasterly winds, but turns anticyclonic when southwesterly winds prevail, indicating strong sensitivity to summer monsoon wind direction. By combining multi-station observations and numerical simulations, this study provides a systematic characterization of the seasonal circulation of the oceanic system in the Beibu Gulf, offering new insights into its dynamic mechanisms. Full article
(This article belongs to the Special Issue Advanced Research on Marine Geology and Sedimentology)
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13 pages, 2593 KiB  
Article
The Effect of Electrode Materials on the Fusion Rate in Multi-State Fusion Reactors
by Mahmoud Bakr, Tom Wallace-Smith, Keisuke Mukai, Edward Martin, Owen Leighton Thomas, Han-Ying Liu, Dali Lemon-Morgan, Erin Holland, Talmon Firestone and Thomas B. Scott
Materials 2025, 18(16), 3734; https://doi.org/10.3390/ma18163734 - 9 Aug 2025
Viewed by 331
Abstract
This study assesses how different anode materials influence neutron production rates (NPRs) in multi-state fusion (MSF) reactors, with a particular focus on the effects of deuterium (D) pre-loading on the anode surface. Three types of mesh anodes were assessed: stainless steel (SS), zirconium [...] Read more.
This study assesses how different anode materials influence neutron production rates (NPRs) in multi-state fusion (MSF) reactors, with a particular focus on the effects of deuterium (D) pre-loading on the anode surface. Three types of mesh anodes were assessed: stainless steel (SS), zirconium (Zr), and D pre-loaded zirconium (ZrD). MSF operates using two electrodes to confine ions to various fusion reactions, including D-D and D-T. The reactor features a negatively biased central cathode and a grounded anode within a vacuum vessel. Neutrons and protons are produced through the application of high voltage (tens of kV) and current (tens of mA) on the system to spark the plasma and start the fusion. Assessments at voltages up to 50 kV and currents up to 30 mA showed that Zr mesh anodes produced higher NPRs than SS ones, reaching 1.912 at 30 kV. This increased performance is attributed to surface fusion processes occurring in the anode. These processes were further modified by the deuterium pre-loading in the ZrD anode, as compared to SS and Zr with 1.832 at 30 kV. The findings suggest that material properties and deuterium pre-loading play significant roles in optimizing the efficiency of MSF reactors and the NPR. Future research may explore the long-term stability and durability of these anode materials under continuous operation conditions to fully harness their potential in fusion energy applications. Full article
(This article belongs to the Section Materials Physics)
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23 pages, 4104 KiB  
Article
A Dynamic Global–Local Spatiotemporal Graph Framework for Multi-City PM2.5 Long-Term Forecasting
by Yao Huang, Xianxun Zhu, Rui Wang, Yanan Xie and Simon Fong
Remote Sens. 2025, 17(16), 2750; https://doi.org/10.3390/rs17162750 - 8 Aug 2025
Viewed by 296
Abstract
Accurate PM2.5 prediction is essential for effective urban air quality management. However, existing methods often struggle to capture the complex, nonlinear, and coupled spatiotemporal dynamics in long-term air pollution evolution. Most existing models rely on short-term observations and overlook long-range temporal trends [...] Read more.
Accurate PM2.5 prediction is essential for effective urban air quality management. However, existing methods often struggle to capture the complex, nonlinear, and coupled spatiotemporal dynamics in long-term air pollution evolution. Most existing models rely on short-term observations and overlook long-range temporal trends and inter-station dependencies, which limit their ability to capture the spatiotemporal evolution of air pollution. To address these challenges, we propose a novel dynamic global–local spatiotemporal graph framework for PM2.5 long-term forecasting across multiple cities. Specifically, we introduce a Multi-Station iTransformer (MS-iTransformer) module to capture long-term temporal dependencies from station-specific historical sequences. To globally model evolving inter-city relationships, we design a bilinear spatiotemporal attention (BSTA) module to adaptively build dynamic spatiotemporal graphs using bilinear spatial and temporal attention. Furthermore, we propose a Graph-Enhanced Spatiotemporal Module (GESM) to capture localized spatiotemporal dependencies through graph convolution and recurrent modeling. The experimental results demonstrate that our model has significant improvements across PM2.5 forecasting tasks on three real-world air quality datasets, outperforming widely adopted baseline approaches. The MAE and RMSE are decreased by 1.7665 and 1.8578, respectively. The FAR is reduced by 0.0312. The CSI and R2 are improved by 0.0194 and 0.0260, respectively. Therefore, the proposed method achieves accurate air quality forecasting by effectively capturing long-term temporal trends, dynamic spatial dependencies, and localized spatiotemporal interactions. Full article
(This article belongs to the Special Issue Remote Sensing and Climate Pollutants)
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19 pages, 28819 KiB  
Article
Dynamical Analysis, Feedback Control Circuit Implementation, and Fixed-Time Sliding Mode Synchronization of a Novel 4D Chaotic System
by Huaigu Tian, Xifeng Yi, Yang Zhang, Zhen Wang, Xiaojian Xi and Jindong Liu
Symmetry 2025, 17(8), 1252; https://doi.org/10.3390/sym17081252 - 6 Aug 2025
Viewed by 231
Abstract
This paper presents a novel four-dimensional (4D) chaotic system exhibiting parametric symmetry breaking and multistability. Through equilibrium stability analysis, attractor reconstruction, Lyapunov Exponent spectra (LEs), and bifurcation diagrams, we reveal a continuous transition from symmetric period attractors to asymmetric chaotic states and rich [...] Read more.
This paper presents a novel four-dimensional (4D) chaotic system exhibiting parametric symmetry breaking and multistability. Through equilibrium stability analysis, attractor reconstruction, Lyapunov Exponent spectra (LEs), and bifurcation diagrams, we reveal a continuous transition from symmetric period attractors to asymmetric chaotic states and rich dynamical behaviors. Additionally, considering the potential of this system in practical applications, a feedback control simulation circuit is designed and implemented to ensure its stability and effectiveness under real-world conditions. Finally, among various control strategies, this paper proposes an innovative Fixed-Time Sliding Mode Synchronization (FTSMS) strategy, determines its synchronization convergence time, and provides an important theoretical foundation for the practical application of the system. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Chaos Theory and Application)
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25 pages, 4865 KiB  
Article
Mathematical Modeling, Bifurcation Theory, and Chaos in a Dusty Plasma System with Generalized (r, q) Distributions
by Beenish, Maria Samreen and Fehaid Salem Alshammari
Axioms 2025, 14(8), 610; https://doi.org/10.3390/axioms14080610 - 5 Aug 2025
Viewed by 191
Abstract
This study investigates the dynamics of dust acoustic periodic waves in a three-component, unmagnetized dusty plasma system using generalized (r,q) distributions. First, boundary conditions are applied to reduce the model to a second-order nonlinear ordinary differential equation. [...] Read more.
This study investigates the dynamics of dust acoustic periodic waves in a three-component, unmagnetized dusty plasma system using generalized (r,q) distributions. First, boundary conditions are applied to reduce the model to a second-order nonlinear ordinary differential equation. The Galilean transformation is subsequently applied to reformulate the second-order ordinary differential equation into an unperturbed dynamical system. Next, phase portraits of the system are examined under all possible conditions of the discriminant of the associated cubic polynomial, identifying regions of stability and instability. The Runge–Kutta method is employed to construct the phase portraits of the system. The Hamiltonian function of the unperturbed system is subsequently derived and used to analyze energy levels and verify the phase portraits. Under the influence of an external periodic perturbation, the quasi-periodic and chaotic dynamics of dust ion acoustic waves are explored. Chaos detection tools confirm the presence of quasi-periodic and chaotic patterns using Basin of attraction, Lyapunov exponents, Fractal Dimension, Bifurcation diagram, Poincaré map, Time analysis, Multi-stability analysis, Chaotic attractor, Return map, Power spectrum, and 3D and 2D phase portraits. In addition, the model’s response to different initial conditions was examined through sensitivity analysis. Full article
(This article belongs to the Special Issue Trends in Dynamical Systems and Applied Mathematics)
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28 pages, 8135 KiB  
Article
Drastically Accelerating Fatigue Life Assessment: A Dual-End Multi-Station Spindle Approach for High-Throughput Precision Testing
by Abdurrahman Doğan, Kürşad Göv and İbrahim Göv
Machines 2025, 13(8), 665; https://doi.org/10.3390/machines13080665 - 29 Jul 2025
Viewed by 435
Abstract
This study introduces a time-efficient rotating bending fatigue testing system featuring 11 dual-end spindles, enabling simultaneous testing of 22 specimens. Designed for high-throughput fatigue life (S–N curve) assessment, the system theoretically allows over 93% reduction in total test duration, with 87.5% savings demonstrated [...] Read more.
This study introduces a time-efficient rotating bending fatigue testing system featuring 11 dual-end spindles, enabling simultaneous testing of 22 specimens. Designed for high-throughput fatigue life (S–N curve) assessment, the system theoretically allows over 93% reduction in total test duration, with 87.5% savings demonstrated in validation experiments using AISI 304 stainless steel. The PLC-based architecture provides autonomous operation, real-time failure detection, and automatic cycle logging. ER16 collet holders are easily replaceable within one minute, and all the components are selected from widely available industrial-grade parts to ensure ease of maintenance. The modular design facilitates straightforward adaptation to different station counts. The validation results confirmed an endurance limit of 421 MPa, which is consistent with the established literature and within ±5% deviation. Fractographic analysis revealed distinct crack initiation and propagation zones, supporting the observed fatigue behavior. This high-throughput methodology significantly improves testing efficiency and statistical reliability, offering a practical solution for accelerated fatigue life evaluation in structural, automotive, and aerospace applications. Full article
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19 pages, 5148 KiB  
Article
Analysis of the Charge Structure Accompanied by Hail During the Development Stage of Thunderstorm on the Qinghai–Tibet Plateau
by Yajun Li, Xiangpeng Fan and Yuxiang Zhao
Atmosphere 2025, 16(8), 906; https://doi.org/10.3390/atmos16080906 - 26 Jul 2025
Viewed by 231
Abstract
The charge structure and lightning activities during the development stage of a thunderstorm with a hail-falling process in Datong County of Qinghai Province on 16 August 2014 were studied by using a multi-station observation network composed of a very-high-frequency, three-dimensional, lightning-radiation-source location system [...] Read more.
The charge structure and lightning activities during the development stage of a thunderstorm with a hail-falling process in Datong County of Qinghai Province on 16 August 2014 were studied by using a multi-station observation network composed of a very-high-frequency, three-dimensional, lightning-radiation-source location system and broadband electric field. The research results show that two discharge regions appeared during the development stage of the thunderstorm. The charge structure was all a negative dipolar polarity in two discharge regions; however, the heights of the charge regions were different. The positive-charge region at a height of 2–3.5 km corresponds to −1–−10 °C and the negative-charge region at a height of 3.5–5 km corresponds to −11–−21 °C in one discharge region; the positive-charge region at a height of 4–5 km corresponds to −15–−21 °C and the negative-charge region at a height of 5–6 km corresponds to −21–−29 °C in another region. The charge regions with the same polarity at different heights in the two discharge regions gradually connected with the occurrence of the hail-falling process during the development stage of the thunderstorm, and the overall height of the charge regions decreased. All the intracloud lightning flashes that occurred in the thunderstorm were of inverted polarity discharge, and the horizontal transmission distance of the discharge channel was short, all within 10 km. The negative intracloud lightning flash, negative cloud-to-ground lightning flash, and positive cloud-to-ground lightning flash generated during the thunderstorm process accounted for 83%, 16%, and 1% of the total number of lightning flashes, respectively. Negative cloud-to-ground lightning flashes mainly occurred more frequently in the early phase of the thunderstorm development stage. As the thunderstorm developed, the frequency of intracloud lightning flashes became greater than that of negative cloud-to-ground lightning flashes, and finally far exceeded it. The frequency of lightning flashes decreases sharply and the intensity of thunderstorms decreases during the hail-falling period. Full article
(This article belongs to the Section Meteorology)
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4 pages, 243 KiB  
Proceeding Paper
Development of High-Speed Rail Demand Forecasting Incorporating Multi-Station Access Probabilities
by Seo-Young Hong and Ho-Chul Park
Eng. Proc. 2025, 102(1), 2; https://doi.org/10.3390/engproc2025102002 - 22 Jul 2025
Viewed by 231
Abstract
This study develops a high-speed rail demand prediction model based on access probability, which quantifies the likelihood of passengers choosing a departure station among multiple alternatives. Traditional models assign demand to the nearest station or rely on manual calibration, often failing to reflect [...] Read more.
This study develops a high-speed rail demand prediction model based on access probability, which quantifies the likelihood of passengers choosing a departure station among multiple alternatives. Traditional models assign demand to the nearest station or rely on manual calibration, often failing to reflect actual travel behavior and requiring excessive time and resources. To address these limitations, this study integrates survey data, real-world datasets, and machine learning techniques to model station choice behavior more accurately. Key influencing factors, including headway, access time, parking availability, and transit connections, were identified through passenger surveys and incorporated into the model. Machine learning algorithms improved prediction accuracy, with SHAP analysis providing interpretability. The proposed model achieved high accuracy, with an average error rate below 3% for major stations. Scenario analyses confirmed its applicability in network expansions, including GTX openings and the integration of mobility as a service. This model enhances data-driven decision-making for rail operators and offers insights for rail network planning and operations. Future research will focus on validating the model across diverse regions and refining it with updated datasets and external data sources. Full article
(This article belongs to the Proceedings of The 2025 Suwon ITS Asia Pacific Forum)
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21 pages, 1359 KiB  
Article
Enhanced Multi-Level Recommender System Using Turnover-Based Weighting for Predicting Regional Preferences
by Venkatesan Thillainayagam, Ramkumar Thirunavukarasu and J. Arun Pandian
Computers 2025, 14(7), 294; https://doi.org/10.3390/computers14070294 - 20 Jul 2025
Viewed by 274
Abstract
In the realm of recommender systems, the prediction of diverse customer preferences has emerged as a compelling research challenge, particularly for multi-state business organizations operating across various geographical regions. Collaborative filtering, a widely utilized recommendation technique, has demonstrated its efficacy in sectors such [...] Read more.
In the realm of recommender systems, the prediction of diverse customer preferences has emerged as a compelling research challenge, particularly for multi-state business organizations operating across various geographical regions. Collaborative filtering, a widely utilized recommendation technique, has demonstrated its efficacy in sectors such as e-commerce, tourism, hotel management, and entertainment-based customer services. In the item-based collaborative filtering approach, users’ evaluations of purchased items are considered uniformly, without assigning weight to the participatory data sources and users’ ratings. This approach results in the ‘relevance problem’ when assessing the generated recommendations. In such scenarios, filtering collaborative patterns based on regional and local characteristics, while emphasizing the significance of branches and user ratings, could enhance the accuracy of recommendations. This paper introduces a turnover-based weighting model utilizing a big data processing framework to mine multi-level collaborative filtering patterns. The proposed weighting model assigns weights to participatory data sources based on the turnover cost of the branches, where turnover refers to the revenue generated through total business transactions conducted by the branch. Furthermore, the proposed big data framework eliminates the forced integration of branch data into a centralized repository and avoids the complexities associated with data movement. To validate the proposed work, experimental studies were conducted using a benchmarking dataset, namely the ‘Movie Lens Dataset’. The proposed approach uncovers multi-level collaborative pattern bases, including global, sub-global, and local levels, with improved predicted ratings compared with results generated by traditional recommender systems. The findings of the proposed approach would be highly beneficial to the strategic management of an interstate business organization, enabling them to leverage regional implications from user preferences. Full article
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20 pages, 2207 KiB  
Review
A Critical Review of the State Estimation Methods of Power Batteries for Electric Vehicles
by Qi Zhang, Hailin Rong, Daduan Zhao, Menglu Pei and Xing Dong
Energies 2025, 18(14), 3834; https://doi.org/10.3390/en18143834 - 18 Jul 2025
Viewed by 393
Abstract
Power batteries and their management technology are crucial for the safe and efficient operation of electric vehicles (EVs). The life and safety issues of power batteries have always plagued the EV industry. To achieve an intelligent battery management system (BMS), it is crucial [...] Read more.
Power batteries and their management technology are crucial for the safe and efficient operation of electric vehicles (EVs). The life and safety issues of power batteries have always plagued the EV industry. To achieve an intelligent battery management system (BMS), it is crucial to accurately estimate the internal state of the power battery. The purpose of this review is to analyze the current status of research on multi-state estimation of power batteries, which mainly focuses on the estimation of state of charge (SOC), state of energy (SOE), state of health (SOH), state of power (SOP), state of temperature (SOT), and state of safety (SOS). Moreover, it also analyzes and prospects the research hotspots, development trends, and future challenges of battery state estimation. It is a significant guide for designing BMSs for EVs, as well as for achieving intelligent safety management and efficient power battery use. Full article
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24 pages, 2394 KiB  
Article
Improving the Reliability of Safety Instrumented Systems Under Degradation with an Alternating Testing Strategy
by Walid Mechri and Christophe Simon
Machines 2025, 13(7), 619; https://doi.org/10.3390/machines13070619 - 17 Jul 2025
Viewed by 316
Abstract
This paper presents an alternating testing strategy to improve the reliability of multi-state safety instrumented systems (SISs) under degradation conditions. A dynamic Bayesian network (DBN) model is developed to assess SIS unavailability, integrating proof-testing parameters and capturing multi-state component behavior. Applied initially to [...] Read more.
This paper presents an alternating testing strategy to improve the reliability of multi-state safety instrumented systems (SISs) under degradation conditions. A dynamic Bayesian network (DBN) model is developed to assess SIS unavailability, integrating proof-testing parameters and capturing multi-state component behavior. Applied initially to the actuator layer of a SIS with a 1oo3 (one-out-of-three) redundancy structure, the study examines the impact of extended test durations, showing that the alternating strategy reduces non-zero test durations compared to the simultaneous test strategy. The approach is then extended to a complete SIS, with a case study demonstrating its potential to enhance system reliability and optimize maintenance management by considering degradation and redundancy factors. Full article
(This article belongs to the Section Machines Testing and Maintenance)
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18 pages, 2823 KiB  
Article
Quasi-Periodic Dynamics and Wave Solutions of the Ivancevic Option Pricing Model Using Multi-Solution Techniques
by Sadia Yasin, Fehaid Salem Alshammari, Asif Khan and Beenish
Symmetry 2025, 17(7), 1137; https://doi.org/10.3390/sym17071137 - 16 Jul 2025
Viewed by 236
Abstract
In this research paper, we study symmetry groups, soliton solutions, and the dynamical behavior of the Ivancevic Option Pricing Model (IOPM). First, we find the Lie symmetries of the considered model; next, we use them to determine the corresponding symmetry groups. Then, we [...] Read more.
In this research paper, we study symmetry groups, soliton solutions, and the dynamical behavior of the Ivancevic Option Pricing Model (IOPM). First, we find the Lie symmetries of the considered model; next, we use them to determine the corresponding symmetry groups. Then, we attempt to solve IOPM by means of two methods. We provide some wave solutions and give further details of the solution using 2D and 3D graphs. These results are interpreted as important clarifications in financial mathematics and deepen our understanding of the dynamics involved during the pricing of options. Secondly, the quasi-periodic behavior of the two-dimensional dynamical system and its perturbed system are plotted using Python software (Python 3.13.5 version). Various frequencies and amplitudes are considered to confirm the quasi-periodic behavior via the Lyapunov exponent, bifurcation diagram, and multistability analysis. These findings are particularly in consonance with current research that investigates IOPM as a nonlinear wave alternate for normal models and the importance of graphical representations in the understanding of financial derivative dynamics. We, therefore, hope to fill in the gaps in the literature that currently exist about the use of multi-solution methods and their effects on financial modeling through the employment of sophisticated graphical techniques. This will be helpful in discussing matters in the field of financial mathematics and open up new directions of investigation. Full article
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