Symmetry

13 pages, 926 KiB

Open AccessReview

Homochirality Emergence: A Scientific Enigma with Profound Implications in Origins of Life Studies

by Michele Fiore

Symmetry 2025, 17(3), 473; https://doi.org/10.3390/sym17030473 - 20 Mar 2025

Viewed by 313

Homochirality, the ubiquitous preference of biological molecules, such as amino acids, sugars, and phospholipids, for a single enantiomeric form, is a fundamental characteristic of life. This consistent bias across the biosphere, where proteins predominantly utilize L-amino acids and nucleic acids predominantly utilize D-sugars, [...] Read more.

Homochirality, the ubiquitous preference of biological molecules, such as amino acids, sugars, and phospholipids, for a single enantiomeric form, is a fundamental characteristic of life. This consistent bias across the biosphere, where proteins predominantly utilize L-amino acids and nucleic acids predominantly utilize D-sugars, is not merely a biochemical peculiarity but a crucial aspect of life’s molecular architecture. However, the origin of this homochirality remains one of the most compelling and unresolved mysteries in the study of life’s origins, drawing inquiry from fields as diverse as cosmology, physics, chemistry, and biology. This article provides an overview of chirality’s pervasive influence across these domains, tracing its potential origins from early Earth’s conditions to its pivotal role in shaping both natural phenomena and the technological advancements that define our future. Full article

(This article belongs to the Special Issue Chemistry: Symmetry/Asymmetry—Feature Papers and Reviews)

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27 pages, 665 KiB

Open AccessArticle

Study of Stability and Simulation for Nonlinear (k, ψ)-Fractional Differential Coupled Laplacian Equations with Multi-Point Mixed (k, ψ)-Derivative and Symmetric Integral Boundary Conditions

by Xiaojun Lv and Kaihong Zhao

Symmetry 2025, 17(3), 472; https://doi.org/10.3390/sym17030472 - 20 Mar 2025

Viewed by 137

Abstract

The

(k, ψ)

-fractional derivative based on the k-gamma function is a more general version of the Hilfer fractional derivative. It is widely used in differential equations to describe physical phenomena, population dynamics, and biological genetic memory problems. In [...] Read more.

The

(k, ψ)

-fractional derivative based on the k-gamma function is a more general version of the Hilfer fractional derivative. It is widely used in differential equations to describe physical phenomena, population dynamics, and biological genetic memory problems. In this article, we mainly study the

4 m + 2

-point symmetric integral boundary value problem of nonlinear

(k, ψ)

-fractional differential coupled Laplacian equations. The existence and uniqueness of solutions are obtained by the Krasnosel’skii fixed-point theorem and Banach’s contraction mapping principle. Furthermore, we also apply the calculus inequality techniques to discuss the stability of this system. Finally, three interesting examples and numerical simulations are given to further verify the correctness and effectiveness of the conclusions. Full article

(This article belongs to the Special Issue Symmetry in Fractional Derivatives, Fractional Equations and Fractional Order Systems)

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18 pages, 4437 KiB

Open AccessArticle

Improved Model-Free Adaptive Predictive Control for Nonlinear Systems with Quantization Under Denial of Service Attacks

by Genfeng Liu, Jinbao Zhu, Yule Wang and Yangyang Wang

Symmetry 2025, 17(3), 471; https://doi.org/10.3390/sym17030471 - 20 Mar 2025

Viewed by 183

Abstract

In this paper, an improved model-free adaptive predictive control method is presented for unknown nonlinear systems with quantization to handle the limited network transmission capacity and denial of service (DoS) attacks. Firstly, to reduce the impact of the DoS attacks on the control [...] Read more.

In this paper, an improved model-free adaptive predictive control method is presented for unknown nonlinear systems with quantization to handle the limited network transmission capacity and denial of service (DoS) attacks. Firstly, to reduce the impact of the DoS attacks on the control system, an attack compensation mechanism is designed, which can be adjusted based on different attack strategies of attackers, and the elastic control of DoS attack can be realized for systems with different complexity and attack intensity. Secondly, a uniform quantizer with encoding and decoding mechanism is presented to tackle the network bandwidth limitation and to reduce the effects of quantization errors. Subsequently, an improved model-free adaptive predictive control method is designed, which can realize the tracking control task of the system with quantization under DoS Attacks. The boundedness of the tracking error of the control system is strictly proved by theoretical analysis. The proposed algorithm has certain symmetry in the prediction time domain and the control time domain. It predicts the state and output of the system at multiple times in the future at each sampling time, and calculates the optimal control sequence according to the predicted results. This kind of symmetric relationship between the prediction of the future and the optimization of the current control is reflected in time, so as to achieve the optimal performance of the system in the whole prediction interval. Finally, the effectiveness and robustness of the presented control method are verified by simulation results under both undisturbed and disturbed conditions. Full article

(This article belongs to the Section Computer)

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Graphical abstract

16 pages, 1377 KiB

Open AccessArticle

Multigrid Methods for Computed Tomography

by Alessandro Buccini, Marco Donatelli and Marco Ratto

Symmetry 2025, 17(3), 470; https://doi.org/10.3390/sym17030470 - 20 Mar 2025

Viewed by 206

Abstract

We consider the problem of computed tomography (CT). This ill-posed inverse problem arises when one wishes to investigate the internal structure of an object with a non-invasive and non-destructive technique. This problem is severely ill-conditioned, meaning it has infinite solutions and is extremely [...] Read more.

We consider the problem of computed tomography (CT). This ill-posed inverse problem arises when one wishes to investigate the internal structure of an object with a non-invasive and non-destructive technique. This problem is severely ill-conditioned, meaning it has infinite solutions and is extremely sensitive to perturbations in the collected data. This sensitivity produces the well-known semi-convergence phenomenon if iterative methods are used to solve it. In this work, we propose a multigrid approach to mitigate this instability and produce fast, accurate, and stable algorithms starting from unstable ones. We consider, in particular, symmetric Krylov methods, like lsqr, as smoother, and a symmetric projection of the coarse grid operator. However, our approach can be extended to any iterative method. Several numerical examples show the performance of our proposal. Full article

(This article belongs to the Section Mathematics)

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29 pages, 1184 KiB

Open AccessReview

AI-Driven Technology in Heart Failure Detection and Diagnosis: A Review of the Advancement in Personalized Healthcare

by Ikteder Akhand Udoy and Omiya Hassan

Symmetry 2025, 17(3), 469; https://doi.org/10.3390/sym17030469 - 20 Mar 2025

Viewed by 698

Abstract

Artificial intelligence (AI) is playing a dominant role in advancing heart failure detection and diagnosis, significantly furthering personalized healthcare. This review synthesizes AI-driven innovations by examining methodologies, applications, and outcomes. We investigate the integration of machine learning algorithms, diverse datasets including electronic health [...] Read more.

Artificial intelligence (AI) is playing a dominant role in advancing heart failure detection and diagnosis, significantly furthering personalized healthcare. This review synthesizes AI-driven innovations by examining methodologies, applications, and outcomes. We investigate the integration of machine learning algorithms, diverse datasets including electronic health records (EHRs), medical records, imaging data, and clinical notes, deep learning models, and neural networks to enhance diagnostic accuracy. Key advancements include prediction models that leverage real-time data from wearable devices alongside state-of-the-art AI systems trained on patient data from hospitals and clinics. Notably, recent studies have reported diagnostic accuracies ranging from 86.7% to as high as 99.9%, with sensitivity and specificity values often exceeding 97%, underscoring the potential of these AI systems to improve early detection and clinical decision-making substantially. Our review further explores the impact of symmetry and asymmetry in model design, highlighting that symmetric architectures like U-Net offer computational efficiency and structured feature extraction. In contrast, asymmetric models improve the sensitivity to rare conditions and subtle clinical patterns. Incorporating these deep learning (DL) methods in anomaly detection and disease progression modeling further reinforces their positive impact on diagnostic accuracy and patient outcomes. Furthermore, this review identifies challenges in current AI applications, such as data quality, algorithmic transparency, model bias, and evaluation metrics, while outlining future research directions, including integrating generative models, hybrid architectures, and explainable AI techniques to optimize clinical practice. Full article

(This article belongs to the Special Issue Asymmetric and Symmetric in Deep Computer Vision and Generative Modeling)

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23 pages, 13777 KiB

Open AccessArticle

The Sine Alpha Power-G Family of Distributions: Characterizations, Regression Modeling, and Applications

by Amani S. Alghamdi, Shatha F. ALoufi and Lamya A. Baharith

Symmetry 2025, 17(3), 468; https://doi.org/10.3390/sym17030468 - 20 Mar 2025

Viewed by 218

Abstract

This study develops a new method for generating families of distributions based on the alpha power transformation and the trigonometric function, which enables enormous versatility in the resulting sub-models and enhances the ability to more accurately characterize tail shapes. This proposed family of [...] Read more.

This study develops a new method for generating families of distributions based on the alpha power transformation and the trigonometric function, which enables enormous versatility in the resulting sub-models and enhances the ability to more accurately characterize tail shapes. This proposed family of distributions is characterized by a single parameter, which exhibits considerable flexibility in capturing asymmetric datasets, making it a valuable alternative to some families of distributions that require additional parameters to achieve similar levels of flexibility. The sine alpha power generated family is introduced using the proposed method, and some of its members and properties are discussed. A particular member, the sine alpha power-Weibull (SAP-W), is investigated in depth. Graphical representations of the new distribution display monotone and non-monotone forms, whereas the hazard rate function takes a reversed J shape, J shape, bathtub, increasing, and decreasing shapes. Various characteristics of SAP-W distribution are derived, including moments, rényi entropies, and order statistics. Parameters of SAP-W are estimated using the maximum likelihood technique, and the effectiveness of these estimators is examined via Monte Carlo simulations. The superiority and potentiality of the proposed approach are demonstrated by analyzing three real-life engineering applications. The SAP-W outperforms several competing models, showing its flexibility. Additionally, a novel-log location-scale regression model is presented using SAP-W. The regression model’s significance is illustrated through its application to real data. Full article

(This article belongs to the Section Mathematics)

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16 pages, 294 KiB

Open AccessArticle

A New Family of Multipartition Graph Operations and Its Applications in Constructing Several Special Graphs

by Qiuping Li, Liangwen Tang, Qingyun Liu and Mugang Lin

Symmetry 2025, 17(3), 467; https://doi.org/10.3390/sym17030467 - 20 Mar 2025

Viewed by 216

Abstract

A new family of graph operations based on multipartite graph with an arbitrary number of parts is defined and their applications are explored in this paper. The complete spectra of graphs derived from multipartite graphs are determined. Because the adjacency matrix of the [...] Read more.

A new family of graph operations based on multipartite graph with an arbitrary number of parts is defined and their applications are explored in this paper. The complete spectra of graphs derived from multipartite graphs are determined. Because the adjacency matrix of the multipartite graph is symmetric, we can use it to generate an unlimited number of special symmetric graphs. Methods for generating countless new families of integral graphs using these multipartite graph operations have been presented. By applying these multipartite graph operations, we can construct infinitely many orderenergetic graphs from orderenergetic or non-orderenergetic graphs. Additionally, infinite pairs of equienergetic and non-cospectral graphs can be generated through these new operations. Moreover, this kind of graph operation can also be used to construct other special graphs related to eigenvalues and energy. Full article

(This article belongs to the Special Issue Symmetry in Combinatorics and Discrete Mathematics)

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19 pages, 3861 KiB

Open AccessArticle

Mechanical Properties of 3D-Printed PLA Structures Observed in Framework of Different Rotational Symmetry Orders in Infill Patterns

by Sanja Mahović Poljaček, Davor Donevski, Tamara Tomašegović, Urška Vrabič Brodnjak and Mirjam Leskovšek

Symmetry 2025, 17(3), 466; https://doi.org/10.3390/sym17030466 - 20 Mar 2025

Viewed by 320

Abstract

In this research, eco-friendly PLA filaments were 3D-printed using FDM. Three geometric shapes with different orders of rotational symmetry were selected to create infill patterns: an equilateral triangle, a square, and a regular hexagon. Additionally, each of these three infill patterns was modified [...] Read more.

In this research, eco-friendly PLA filaments were 3D-printed using FDM. Three geometric shapes with different orders of rotational symmetry were selected to create infill patterns: an equilateral triangle, a square, and a regular hexagon. Additionally, each of these three infill patterns was modified by rotating the basic shape used to form the infill pattern by 0°, 15°, and 30°. The objective of this study was to analyze how the order of rotational symmetry within the infill pattern affects the mechanical properties of the printed specimens. To ensure consistency, infill density was kept as uniform as possible across all samples produced. DMA and tensile tests were performed on the produced specimens. The obtained mean values in the tensile measurements were compared using the Kruskal–Wallis test. Dunn’s test was used for post hoc pairwise multiple comparisons. DMA showed that when comparing different infill patterns, the specimens with an order of rotational symmetry of 3 (triangle) showed the highest modulus of elasticity, and the specimens with a 15° rotation regardless of shape generally had the highest storage modulus. Statistical analysis showed that the maximum force of the infill pattern with an order of rotational symmetry of 3 (triangle) was the least affected by the rotation angle, while the infill pattern with an order of rotational symmetry of 4 (square) and a 0° rotation displayed a significantly higher value of the maximum force than other patterns. The infill pattern with an order of rotational symmetry of 6 (hexagon) was moderately affected by the angle of rotation. Given the numerous infill patterns utilized in FDM, the results of this research offered a new viewpoint and insights into optimizing the mechanical properties of 3D-printed infill patterns. Full article

(This article belongs to the Section Engineering and Materials)

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20 pages, 7458 KiB

Open AccessArticle

Structural Damage Identification Using Data Fusion and Optimization of the Self-Adaptive Differential Evolution Algorithm

by Yajun Li, Changsheng Xiang, Edoardo Patelli and Hua Zhao

Symmetry 2025, 17(3), 465; https://doi.org/10.3390/sym17030465 - 20 Mar 2025

Viewed by 240

Abstract

This paper addresses the critical challenges of inadequate localization and low quantification precision in structural damage identification by introducing a novel approach that integrates Dempster–Shafer (D-S) evidence theory with the Self-Adaptive Differential Evolution (SDE) algorithm. First, modal parameters are extracted from a simply [...] Read more.

This paper addresses the critical challenges of inadequate localization and low quantification precision in structural damage identification by introducing a novel approach that integrates Dempster–Shafer (D-S) evidence theory with the Self-Adaptive Differential Evolution (SDE) algorithm. First, modal parameters are extracted from a simply supported beam using the finite element (FE) method, and the corresponding index values are computed based on the formulated damage identification index equations. Next, these indices are applied to analyze damage localization in both single-position and multi-position scenarios within the simply supported beam. The SDE algorithm is then employed to dynamically optimize the initial weights and thresholds of various algorithms, ensuring the assignment of optimal values. Finally, the resulting data are input into the model for training, yielding a prediction model with enhanced accuracy that can precisely estimate the damage severity of the simply supported beam. The findings demonstrate that the three proposed damage identification indices—DI_1,i,j, DI_2,i,j, and DSDI_i,j—not only achieve high accuracy in damage localization but also significantly improve the precision of algorithms optimized by the SDE. These methods exhibit strong accuracy and robustness, providing a valuable reference for damage identification in small-to-medium-span simply supported beam bridges. Full article

(This article belongs to the Section Mathematics)

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16 pages, 12825 KiB

Open AccessArticle

Stability Analysis of Parametric Vibration in Overhead Conductors Under Time-Varying Tension

by Xiaojuan Chen, Mengyang Han, Xiaolong Yang and Bo Wang

Symmetry 2025, 17(3), 464; https://doi.org/10.3390/sym17030464 - 20 Mar 2025

Cited by 1 | Viewed by 241

Abstract

This paper investigates the impact of dynamic tension induced by adjacent span vibrations on the vibrational characteristics of overhead conductors. A simplified model is established, considering the overhead conductor with a symmetric structure as a simply supported flexible long wire subjected to axial [...] Read more.

This paper investigates the impact of dynamic tension induced by adjacent span vibrations on the vibrational characteristics of overhead conductors. A simplified model is established, considering the overhead conductor with a symmetric structure as a simply supported flexible long wire subjected to axial time-varying tension at one end. The transverse motion partial differential equation of the overhead conductor under time-varying tension is formulated and discretized into a parametric vibration equation with time-varying coefficients using the Galerkin method. Based on Floquet theory, the study systematically analyzes the influence of time-varying tension on system stability, delineates the boundaries of parametric resonance instability regions, and conducts time-history analysis of vibrational responses within these regions. The research demonstrates that when the frequency of the time-varying tension approaches the line’s natural frequency or its double, the system is prone to instability. While the damping coefficient can enhance system stability, it has limited effectiveness in suppressing the primary instability region. The study found that the vibrational responses of parametric vibrations exhibit nearly symmetric distributions within the instability regions and along the critical boundaries. Adjusting the frequency differences between adjacent spans effectively mitigates the parametric resonance issues in overhead conductors, providing valuable insights for engineering design. Full article

(This article belongs to the Section Engineering and Materials)

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17 pages, 295 KiB

Open AccessArticle

Discrete-Time Dynamical Systems on Structured State Spaces: State-Transition Laws in Finite-Dimensional Lie Algebras

by Simone Fiori

Symmetry 2025, 17(3), 463; https://doi.org/10.3390/sym17030463 - 19 Mar 2025

Cited by 1 | Viewed by 174

Abstract

The present paper elaborates on the development of a theory of discrete-time dynamical systems on finite-dimensional structured state spaces. Dynamical systems on structured state spaces possess well-known applications to solving differential equations in physics, and it was shown that discrete-time systems on finite- [...] Read more.

The present paper elaborates on the development of a theory of discrete-time dynamical systems on finite-dimensional structured state spaces. Dynamical systems on structured state spaces possess well-known applications to solving differential equations in physics, and it was shown that discrete-time systems on finite- (albeit high-) dimensional structured state spaces possess solid applications to structured signal processing and nonlinear system identification, modeling and control. With reference to the state-space representation of dynamical systems, the present contribution tackles the core system-theoretic problem of determining suitable laws to express a system’s state transition. In particular, the present contribution aims at formulating a fairly general class of state-transition laws over the Lie algebra associated to a Lie group and at extending some properties of classical dynamical systems to process Lie-algebra-valued state signals. Full article

(This article belongs to the Special Issue Symmetry and Lie Algebras)

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22 pages, 7677 KiB

Open AccessArticle

Universal Low-Frequency Noise Black-Box Attack on Visual Object Tracking

by Hanting Hou, Huan Bao, Kaimin Wei and Yongdong Wu

Symmetry 2025, 17(3), 462; https://doi.org/10.3390/sym17030462 - 19 Mar 2025

Viewed by 252

Abstract

Adversarial attacks on visual object tracking aim to degrade tracking accuracy by introducing imperceptible perturbations into video frames, exploiting vulnerabilities in neural networks. In real-world symmetrical double-blind engagements, both attackers and defenders operate with mutual unawareness of strategic parameters or initiation timing. Black-box [...] Read more.

Adversarial attacks on visual object tracking aim to degrade tracking accuracy by introducing imperceptible perturbations into video frames, exploiting vulnerabilities in neural networks. In real-world symmetrical double-blind engagements, both attackers and defenders operate with mutual unawareness of strategic parameters or initiation timing. Black-box attacks based on iterative optimization show excellent applicability in this scenario. However, existing state-of-the-art adversarial attacks based on iterative optimization suffer from high computational costs and limited effectiveness. To address these challenges, this paper proposes the Universal Low-frequency Noise black-box attack method (ULN), which generates perturbations through discrete cosine transform to disrupt structural features critical for tracking while mimicking compression artifacts. Extensive experimentation on four state-of-the-art trackers, including transformer-based models, demonstrates the method’s severe degradation effects. GRM’s expected average overlap drops by

97.77 %

on VOT2018, while SiamRPN++’s AUC and Precision on OTB100 decline by

76.55 %

and

78.9 %

, respectively. The attack achieves real-time performance with a computational cost reduction of over

50 %

compared to iterative methods, operating efficiently on embedded devices such as Raspberry Pi 4B. By maintaining a structural similarity index measure above

0.84

, the perturbations blend seamlessly with common compression artifacts, evading traditional spatial filtering defenses. Cross-platform experiments validate its consistent threat across diverse hardware environments, with attack success rates exceeding

40 %

even under resource constraints. These results underscore the dual capability of ULN as both a stealthy and practical attack vector, and emphasize the urgent need for robust defenses in safety-critical applications such as autonomous driving and aerial surveillance. The efficiency of the method, when combined with its ability to exploit low-frequency vulnerabilities across architectures, establishes a new benchmark for adversarial robustness in visual tracking systems. Full article

(This article belongs to the Section Computer)

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26 pages, 29021 KiB

Open AccessArticle

Efficient Coastal Mangrove Species Recognition Using Multi-Scale Features Enhanced by Multi-Head Attention

by Shaolin Guo, Yixuan Wang, Yin Tan, Tonglai Liu and Qin Qin

Symmetry 2025, 17(3), 461; https://doi.org/10.3390/sym17030461 - 19 Mar 2025

Viewed by 224

Abstract

Recognizing mangrove species is a challenging task in coastal wetland ecological monitoring due to the complex environment, high species similarity, and the inherent symmetry within the structural features of mangrove species. Many species coexist, exhibiting only subtle differences in leaf shape and color, [...] Read more.

Recognizing mangrove species is a challenging task in coastal wetland ecological monitoring due to the complex environment, high species similarity, and the inherent symmetry within the structural features of mangrove species. Many species coexist, exhibiting only subtle differences in leaf shape and color, which increases the risk of misclassification. Additionally, mangroves grow in intertidal environments with varying light conditions and surface reflections, further complicating feature extraction. Small species are particularly hard to distinguish in dense vegetation due to their symmetrical features that are difficult to differentiate at the pixel level. While hyperspectral imaging offers some advantages in species recognition, its high equipment costs and data acquisition complexity limit its practical application. To address these challenges, we propose MHAGFNet, a segmentation-based mangrove species recognition network. The network utilizes easily accessible RGB remote sensing images captured by drones, ensuring efficient data collection. MHAGFNet integrates a Multi-Scale Feature Fusion Module (MSFFM) and a Multi-Head Attention Guide Module (MHAGM), which enhance species recognition by improving feature capture across scales and integrating both global and local details. In this study, we also introduce MSIDBG, a dataset created using high-resolution UAV images from the Shankou Mangrove National Nature Reserve in Beihai, China. Extensive experiments demonstrate that MHAGFNet significantly improves accuracy and robustness in mangrove species recognition. Full article

(This article belongs to the Section Computer)

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23 pages, 509 KiB

Open AccessArticle

Functional Time Series Analysis Using Single-Index L¹-Modal Regression

by Mohammed B. Alamari, Fatimah A. Almulhim, Zoulikha Kaid and Ali Laksaci

Symmetry 2025, 17(3), 460; https://doi.org/10.3390/sym17030460 - 19 Mar 2025

Viewed by 179

Abstract

A new predictor in functional time series (FTS ) is considered. It is based on the asymmetric weighting function of quantile regression. More precisely, we assume that FTS is generated from a single-index model that permits the observation of endogenous–exogenous variables by combining [...] Read more.

A new predictor in functional time series (FTS ) is considered. It is based on the asymmetric weighting function of quantile regression. More precisely, we assume that FTS is generated from a single-index model that permits the observation of endogenous–exogenous variables by combining the nonparametric model with a linear one. In parallel, the

L^{1}

-modal predictor is estimated using the M-estimation of the derivative of the conditional quantile of the generated FTS. In the mathematical part, we prove the complete convergence of the constructed estimator, and we determine its convergence rate. An empirical analysis is performed to prove the applicability of the estimator and to evaluate the impact of different structures involved in the smoothing approach. This analysis is carried out using simulated and real data. Finally, the regressive nature of the constructed predictor allows it to provide a robust instantaneous predictor for environmental data. Full article

(This article belongs to the Section Mathematics)

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18 pages, 9208 KiB

Open AccessArticle

Short Circuit Fault Detection in DAR Based on V-I Characteristic Graph and Machine Learning

by Junlin Zhu, Jiahui Yang, Xiaojing Dang, Xiaqing Sun, Wei Zhang, Yuqian Song and Zhongyong Zhao

Symmetry 2025, 17(3), 459; https://doi.org/10.3390/sym17030459 - 19 Mar 2025

Viewed by 199

Abstract

Dry-type air-core reactors (DAR) are critical components in power systems but are prone to inter-turn short circuit faults which interrupt the symmetry of the winding structure. Inspired by the online detection of transformer winding deformation, the V-I method has been adapted to diagnose [...] Read more.

Dry-type air-core reactors (DAR) are critical components in power systems but are prone to inter-turn short circuit faults which interrupt the symmetry of the winding structure. Inspired by the online detection of transformer winding deformation, the V-I method has been adapted to diagnose short circuit faults in reactors. However, the diagnostic criteria and thresholds of V-I method remain unclear. This paper presents a novel method for determining the threshold for detecting inter-turn short circuit faults in DAR, integrating V-I analysis with machine learning techniques. Specifically, Gradient Boosting Regression (GBR) is used to compute a standard diagnostic criterion value, and curve fitting is also used to define the threshold for identifying inter-turn short circuit faults. The experimental results demonstrate that this method effectively identifies fault conditions in DAR. Full article

(This article belongs to the Section Engineering and Materials)

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20 pages, 447 KiB

Open AccessArticle

Enhancing Quantum Key Distribution Security Through Hybrid Protocol Integration

by Suhare Solaiman

Symmetry 2025, 17(3), 458; https://doi.org/10.3390/sym17030458 - 18 Mar 2025

Viewed by 286

Abstract

With the increasing complexity of cyber threats and the emergence of quantum computing, enhancing secure communication is essential. This study explores an effective hybrid quantum key distribution (QKD) protocol that integrates photonic and atomic systems to leverage their respective strengths. The concept of [...] Read more.

With the increasing complexity of cyber threats and the emergence of quantum computing, enhancing secure communication is essential. This study explores an effective hybrid quantum key distribution (QKD) protocol that integrates photonic and atomic systems to leverage their respective strengths. The concept of symmetry plays a crucial role in this context, as it underpins the principles of entanglement and the balance between key generation and error correction. The photonic system is used for the initial key generation, while the atomic system facilitates entanglement swapping, error correction, and privacy amplification. The comprehensive theoretical framework encompasses key components, detailed security proofs, performance metrics, and an analysis of system vulnerabilities, illustrating the resilience of the hybrid protocol against potential threats. Extensive experimental studies demonstrate that the hybrid QKD protocol seamlessly integrates photonic and atomic systems, enabling secure key distribution with minimal errors and loss rates over long distances. This combination of the two systems reveals exceptional resilience against eavesdropping, significantly improving both security and robustness compared with traditional QKD protocols. Consequently, this makes it a compelling solution for secure communication in the increasingly digital world. Full article

(This article belongs to the Section Computer)

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32 pages, 1098 KiB

Open AccessArticle

Estimation and Bayesian Prediction for New Version of Xgamma Distribution Under Progressive Type-II Censoring

by Ahmed R. El-Saeed, Molay Kumar Ruidas and Ahlam H. Tolba

Symmetry 2025, 17(3), 457; https://doi.org/10.3390/sym17030457 - 18 Mar 2025

Viewed by 155

Abstract

This article introduces a new continuous lifetime distribution within the Gamma family, called the induced Xgamma distribution, and explores its various statistical properties. The proposed distribution’s estimation and prediction are investigated using Bayesian and non-Bayesian approaches under progressively Type-II censored data. The maximum [...] Read more.

This article introduces a new continuous lifetime distribution within the Gamma family, called the induced Xgamma distribution, and explores its various statistical properties. The proposed distribution’s estimation and prediction are investigated using Bayesian and non-Bayesian approaches under progressively Type-II censored data. The maximum likelihood and maximum product spacing methods are applied for the non-Bayesian approach, and some of their performances are evaluated. In the Bayesian framework, the numerical approximation technique utilizing the Metropolis–Hastings algorithm within the Markov chain Monte Carlo is employed under different loss functions, including the squared error loss, general entropy, and LINEX loss. Interval estimation methods, such as asymptotic confidence intervals, log-normal asymptotic confidence intervals, and highest posterior density intervals, are also developed. A comprehensive numerical study using Monte Carlo simulations is conducted to evaluate the performance of the proposed point and interval estimation methods through progressive Type-II censored data. Furthermore, the applicability and effectiveness of the proposed distribution are demonstrated through three real-world datasets from the fields of medicine and engineering. Full article

(This article belongs to the Special Issue Bayesian Statistical Methods for Forecasting)

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22 pages, 24537 KiB

Open AccessArticle

Recovery-Enhanced Image Steganography Framework with Auxiliary Model Based on Invertible Neural Networks

by Lin Huo, Kai Wang and Jie Wei

Symmetry 2025, 17(3), 456; https://doi.org/10.3390/sym17030456 - 18 Mar 2025

Viewed by 244

Abstract

With the advancement of technology, the information hiding capacity has significantly increased, allowing a cover image to conceal one or more secret images. However, this high hiding capacity often leads to contour shadows and color distortions, making the high-quality recovery of secret images [...] Read more.

With the advancement of technology, the information hiding capacity has significantly increased, allowing a cover image to conceal one or more secret images. However, this high hiding capacity often leads to contour shadows and color distortions, making the high-quality recovery of secret images extremely challenging. Existing image hiding algorithms based on Invertible Neural Networks (INNs) often discard useful information during the hiding process, resulting in poor quality of the recovered secret images, especially in multi-image hiding scenarios. The theoretical symmetry of INNs ensures the lossless reversibility of the embedder and decoder, but the lost information generated in practical image steganography disrupts this symmetry. To address this issue, we propose an INN-based image steganography framework that overcomes the limitations of current INN methods in image steganography applications. Our framework can embed multiple full-size secret images into cover images of the same size and utilize the correlation between the lost information and the secret and cover images to generate the lost information by combining the auxiliary model of the Dense–Channel–Spatial Attention Module to restore the symmetry of reversible neural networks, thereby improving the quality of the recovered images. In addition, we employ a multi-stage progressive training strategy to improve the recovery of lost information, thereby achieving high-quality secret image recovery. To further enhance the security of the hiding process, we introduced a multi-scale wavelet loss function into the loss function. Our method significantly improves the quality of image recovery in single-image steganography tasks across multiple datasets (DIV2K, COCO, ImageNet), with a PSNR reaching up to 50.37 dB (an improvement of over 3 dB compared to other methods). The results show that our method outperforms other state-of-the-art (SOTA) image hiding techniques on different datasets and achieves strong performance in multi-image hiding as well. Full article

(This article belongs to the Section Computer)

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20 pages, 10313 KiB

Open AccessArticle

Fractional Order Curves

by Marius-F. Danca and Jagan Mohan Jonnalagadda

Symmetry 2025, 17(3), 455; https://doi.org/10.3390/sym17030455 - 18 Mar 2025

Viewed by 149

Abstract

This paper continues the subject of symmetry breaking of fractional-order maps, previously addressed by one of the authors. Several known planar classes of curves of integer order are considered and transformed into their fractional order. Several known planar classes of curves of integer [...] Read more.

This paper continues the subject of symmetry breaking of fractional-order maps, previously addressed by one of the authors. Several known planar classes of curves of integer order are considered and transformed into their fractional order. Several known planar classes of curves of integer order are considered and transformed into their fractional order. For this purpose, the Grunwald–Letnikov numerical scheme is used. It is shown numerically that the aesthetic appeal of most of the considered curves of integer order is broken when the curves are transformed into fractional-order variants. The considered curves are defined by parametric representation, Cartesian representation, and iterated function systems. To facilitate the numerical implementation, most of the curves are considered under their affine function representation. In this way, the utilized iterative algorithm can be easily followed. Besides histograms, the entropy of a curve, a useful numerical tool to unveil the characteristics of the obtained fractional-order curves and to compare them with their integer-order counterparts, is used. A Matlab code is presented that can be easily modified to run for all considered curves. Full article

(This article belongs to the Section Mathematics)

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15 pages, 335 KiB

Open AccessArticle

On the Secant Non-Defectivity of Integral Hypersurfaces of Projective Spaces of at Most Five Dimensions

by Edoardo Ballico

Symmetry 2025, 17(3), 454; https://doi.org/10.3390/sym17030454 - 18 Mar 2025

Viewed by 129

Abstract

Let

X \subset P^{n}

, where

3 \leq n \leq 5

, be an irreducible hypersurface of degree

d \geq 2

. Fix an integer

t \geq 3

. If

n = 5

, assume

t \geq 4

and [...] Read more.

Let

X \subset P^{n}

, where

3 \leq n \leq 5

, be an irreducible hypersurface of degree

d \geq 2

. Fix an integer

t \geq 3

. If

n = 5

, assume

t \geq 4

and

(t, d) \neq (4, 2)

. Using the Differential Horace Lemma, we prove that

O_{X} (t)

is not secant defective. For a fixed X, our proof uses induction on the integer t. The key points of our method are that for a fixed X, we only need the case of general linear hyperplane sections of X in lower-dimension projective spaces and that we do not use induction on d, allowing an interested reader to tackle a specific X for

n > 5

. We discuss (as open questions) possible extensions of some weaker forms of the theorem to the case where

n > 5

. Full article

(This article belongs to the Special Issue Mathematics: Feature Papers 2025)

14 pages, 232 KiB

Open AccessArticle

Finding the Integral-Equation-Based Linear Renewal Density Equation and Analytical Solutions

by Muharrem Tuncay Gençoğlu

Symmetry 2025, 17(3), 453; https://doi.org/10.3390/sym17030453 - 18 Mar 2025

Viewed by 168

Abstract

In this study, the linear renewal equation is obtained by using the integral equation, the renewal function and the Fourier–Stieltjes transform. It is proven that the linear renewal equation can be obtained by taking the derivative of the integral equation. Analytical methods for [...] Read more.

In this study, the linear renewal equation is obtained by using the integral equation, the renewal function and the Fourier–Stieltjes transform. It is proven that the linear renewal equation can be obtained by taking the derivative of the integral equation. Analytical methods for the solution of the obtained linear renewal equation are discussed. It is shown that the linear renewal equation is a powerful tool that can model the direct relationship between stochastic processes and density functions. It is shown that the Fourier–Stieltjes transform allows the equation to be simplified in the frequency domain and analytical solutions to be obtained, and the Laplace transform provides an effective analytical solution method, especially for uniform distribution and exponential density functions. The integral equation-based linear renewal density equation derived in this study preserves the temporal and structural symmetries of the system, allowing for the analytical derivation of symmetric forms in the solution space. In the light of the findings, predictions were made about what kind of studies would be done in the future. Full article

(This article belongs to the Special Issue Nonlinear Differential and Integral Equations and Their Infinite Systems)

24 pages, 4704 KiB

Open AccessArticle

An Unconditionally Stable Numerical Scheme for 3D Coupled Burgers’ Equations

by Gonca Çelikten

Symmetry 2025, 17(3), 452; https://doi.org/10.3390/sym17030452 - 18 Mar 2025

Viewed by 146

Abstract

In this study, we sought numerical solutions for three-dimensional coupled Burgers’ equations. Burgers’ equations are fundamental partial differential equations in fluid mechanics. They integrate the characteristics of both the first-order wave equation and the heat conduction equation, serving as crucial tools for modeling [...] Read more.

In this study, we sought numerical solutions for three-dimensional coupled Burgers’ equations. Burgers’ equations are fundamental partial differential equations in fluid mechanics. They integrate the characteristics of both the first-order wave equation and the heat conduction equation, serving as crucial tools for modeling the interaction between convection and diffusion. First, the fractional step method was applied to decompose the equations into one-dimensional forms. Then, implicit finite difference approximations were used to solve the resulting one-dimensional equations. To assess the accuracy of the proposed approach, we tested it on two benchmark problems and compared the results with existing methods in the literature. Additionally, the symmetry of the solution graphs was analyzed to gain deeper insight into the results. Stability analysis using the von Neumann method confirmed that the proposed approach is unconditionally stable. The results obtained in this study strongly support the effectiveness and reliability of the proposed method in solving three-dimensional coupled Burgers’ equations. Full article

(This article belongs to the Special Issue Symmetry in Fluid Mechanics: New Challenges in Fluid–Structure Interaction)

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14 pages, 1070 KiB

Open AccessArticle

Efficient Numerical Techniques for Investigating Chaotic Behavior in the Fractional-Order Inverted Rössler System

by Mohamed Elbadri, Dalal M. AlMutairi, D. K. Almutairi, Abdelgabar Adam Hassan, Walid Hdidi and Mohamed A. Abdoon

Symmetry 2025, 17(3), 451; https://doi.org/10.3390/sym17030451 - 18 Mar 2025

Viewed by 259

Abstract

In this study, the numerical scheme for the Caputo fractional derivative (NCFD) method and the He–Laplace method (H-LM) are two powerful methods used for analyzing fractional-order systems. These two approaches are used in the study of the complex dynamics of the fractional-order inverted [...] Read more.

In this study, the numerical scheme for the Caputo fractional derivative (NCFD) method and the He–Laplace method (H-LM) are two powerful methods used for analyzing fractional-order systems. These two approaches are used in the study of the complex dynamics of the fractional-order inverted Rössler system, particularly for the detection of chaotic behavior. The enhanced NCFD method is used for reliable and accurate numerical simulations by capturing the intricate dynamics of chaotic systems. Further, analytical solutions are obtained using the H-LM for the fractional-order inverted Rössler system. This method is popular due to its simplicity, numerical stability, and ability to handle most initial values, yielding very accurate results. Combining analytical insights from the H-LM with the robust numerical accuracy of the NCFD approach yields a comprehensive understanding of this system’s dynamics. The advantages of the NCFD method include its high numerical accuracy and ability to capture complex chaotic dynamics. The H-LM offers simplicity and stability. The proposed methods prove to be capable of detecting chaotic attractors, estimating their behavior correctly, and finding accurate solutions. These findings confirm that NCFD- and H-LM-based approaches are promising methods for the modeling and solution of complex systems. Since these results provide improved numerical simulations and solutions for a broad class of fractional-order models, they will thus be of greatest use in forthcoming applications in engineering and science. Full article

(This article belongs to the Special Issue Symmetry and Its Applications in Partial Differential Equations)

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13 pages, 949 KiB

Open AccessArticle

Algebraic and Spectral Analysis of a Novel Hermitian Spin Basis

by Timothy Ganesan, Zeeshan Yousaf and M. Z. Bhatti

Symmetry 2025, 17(3), 450; https://doi.org/10.3390/sym17030450 - 17 Mar 2025

Viewed by 647

Abstract

This work aims to explore the algebraic and spectral properties of a novel parametric Hermitian non-Pauli spin basis. The primary motivation for this work is to introduce an alternative to the Pauli spin basis for investigating systems where conventional quantum statistics no longer [...] Read more.

This work aims to explore the algebraic and spectral properties of a novel parametric Hermitian non-Pauli spin basis. The primary motivation for this work is to introduce an alternative to the Pauli spin basis for investigating systems where conventional quantum statistics no longer apply. This study explores the symmetries, commutation relations, Lie algebra structures, and ladder operators of the proposed spin matrices. Additionally, it provides discussions on key findings, potential applications, and concludes with some final remarks. An example for modeling the spectrum of a quantum system is provided. Full article

(This article belongs to the Section Mathematics)

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22 pages, 2531 KiB

Open AccessArticle

An Improved Self-Organizing Map (SOM) Based on Virtual Winning Neurons

by Xiaoliang Fan, Shaodong Zhang, Xuefeng Xue, Rui Jiang, Shuwen Fan and Hanliang Kou

Symmetry 2025, 17(3), 449; https://doi.org/10.3390/sym17030449 - 17 Mar 2025

Viewed by 225

Abstract

Self-Organizing Map (SOM) neural networks can project complex, high-dimensional data onto a two-dimensional plane for data visualization, enabling an intuitive understanding of the distribution and symmetric structures of such data, thereby facilitating the clustering and anomaly detection of complex high-dimensional data. However, this [...] Read more.

Self-Organizing Map (SOM) neural networks can project complex, high-dimensional data onto a two-dimensional plane for data visualization, enabling an intuitive understanding of the distribution and symmetric structures of such data, thereby facilitating the clustering and anomaly detection of complex high-dimensional data. However, this algorithm is sensitive to the initial weight matrix and suffers from insufficient feature extraction. To address these issues, this paper proposes an improved SOM based on virtual winning neurons (virtual-winner SOMs, vwSOMs). In this method, the principal component analysis (PCA) is utilized to generate the initial weight matrix, allowing the weights to better capture the main features of the data and thereby enhance clustering performance. Subsequently, when new input sample data are mapped to the output layer, multiple neurons with a high similarity in the weight matrix are selected to calculate a virtual winning neuron, which is then used to update the weight matrix to comprehensively represent the input data features within a minimal error range, thus improving the algorithm’s robustness. Multiple datasets were used to analyze the clustering performance of vwSOM. On the Iris dataset, the S is 0.5262, the F1 value is 0.93, the ACC value is 0.9412, and the VA is 0.0012, and the experimental result with the Wine dataset shows that the S is 0.5255, the F1 value is 0.93, the ACC value is 0.9401, and the VA is 0.0014. Finally, to further demonstrate the performance of the algorithm, we use the more complex Waveform dataset; the S is 0.5101, the F1 value is 0.88, the ACC value is 0.8931, and the VA is 0.0033. All the experimental results show that the proposed algorithm can significantly improve clustering accuracy and have better stability, and its algorithm complexity can meet the requirements for real-time data processing. Full article

(This article belongs to the Special Issue Advances in Machine Learning and Symmetry/Asymmetry)

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24 pages, 6036 KiB

Open AccessArticle

An Improved Set-Valued Observer and Probability Density Function-Based Self-Organizing Neural Networks for Early Fault Diagnosis in Wind Energy Conversion Systems

by Ruinan Zhao

Symmetry 2025, 17(3), 448; https://doi.org/10.3390/sym17030448 - 17 Mar 2025

Viewed by 147

Abstract

Fault diagnosis is crucial for ensuring the reliability and safety of wind energy conversion systems (WECSs). However, existing methods are often specific to components or specific types of wind turbines and face challenges, such as difficulty in threshold setting and low accuracy in [...] Read more.

Fault diagnosis is crucial for ensuring the reliability and safety of wind energy conversion systems (WECSs). However, existing methods are often specific to components or specific types of wind turbines and face challenges, such as difficulty in threshold setting and low accuracy in diagnosing faults at early stages. To address these challenges, this paper proposes a novel fault diagnosis method based on self-organizing neural networks (SONNs) and probability density functions (PDFs). First, an improved set-valued observer (ISVO) is designed to accurately estimate the states of WECSs, considering the time delay and unknown nonlinearity of overall model. Then, the PDF is derived by fitting the estimation error data to characterize three common multiplicative faults of the pitch system actuators. Two types of SONNs are developed to cluster the parameter sets of the PDF. Finally, the PDFs of the estimation error are reconstructed based on the clustering results, thereby designing fault diagnosis strategies that enable a rapid and highly accurate diagnosis of early-stage faults. Simulation results demonstrate that the proposed strategies achieved an early fault diagnosis accuracy rate of over 90%, with the fastest diagnosis time being approximately 0.11 s. Under the same fault conditions, the diagnosis time is 1 s faster than that of a k-means-based fault diagnosis strategy. This study provides a threshold-free, high-accuracy, and rapid fault diagnosis strategy for early fault diagnosis in WECS. By combining neural networks, the proposed method addresses the issue of threshold dependency in fault diagnosis, with potential applications in improving the reliability and safety of wind power generation. Full article

(This article belongs to the Section Computer)

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25 pages, 6881 KiB

Open AccessArticle

Evaluation on the Global Response Characteristics of a Rotor/Stator Rubbing System: Experiment and Dynamic Simulation

by Shunzeng Wang, Yang Li and Xiaoming Liu

Symmetry 2025, 17(3), 447; https://doi.org/10.3390/sym17030447 - 17 Mar 2025

Viewed by 150

Abstract

The global response characteristics of rotor/stator rubbing systems are critical for the optimal design and safe operation of rotating machinery. Based on the mathematical model, numerical simulation and theoretical analysis have been widely carried out to study the regions of different responses, which [...] Read more.

The global response characteristics of rotor/stator rubbing systems are critical for the optimal design and safe operation of rotating machinery. Based on the mathematical model, numerical simulation and theoretical analysis have been widely carried out to study the regions of different responses, which have not been globally explored and evaluated by experiments with the unified parameters of a mathematical and physical model. Thus, the existence conditions of the global responses of a rubbing rotor are experimentally investigated and then quantitatively compared with theoretical solutions and dynamic simulation results. With the equivalent stiffness and the kinetic dry friction identified by the aid of a new voltage divider, the rubbing rotors are accurately tested by the new experimental technique and dynamically simulated by rigid-flexible coupling technique. From the comparison results of orbit and full spectrum, it is shown that the response characteristics of no rub motion, synchronous full annular rub, partial rub, and dry friction backward whirl obtained by experiment and dynamic simulation are in good agreement with theoretical solutions. Then, it is also concluded that all boundaries of the existence/co-existence regions of the whirling motions are proved to be valid. Moreover, stick-slip oscillation is detected in the rotor/stator testing system. Full article

(This article belongs to the Section Engineering and Materials)

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17 pages, 270 KiB

Open AccessArticle

On the Oscillatory Behavior of a Class of Mixed Fractional-Order Nonlinear Differential Equations

by George E. Chatzarakis, N. Nagajothi, M. Deepa and Vadivel Sadhasivam

Symmetry 2025, 17(3), 446; https://doi.org/10.3390/sym17030446 - 17 Mar 2025

Viewed by 151

Abstract

This paper investigates the oscillatory behavior of a class of mixed fractional-order nonlinear differential equations incorporating both the Liouville right-sided and conformable fractional derivatives. Symmetry plays a key role in understanding the oscillatory behavior of these systems. The motivation behind this study arises [...] Read more.

This paper investigates the oscillatory behavior of a class of mixed fractional-order nonlinear differential equations incorporating both the Liouville right-sided and conformable fractional derivatives. Symmetry plays a key role in understanding the oscillatory behavior of these systems. The motivation behind this study arises from the need for a more generalized framework to analyze oscillatory behavior in fractional differential equations, bridging the gap in the existing literature. By employing the generalized Riccati technique and the integral averaging method, we establish new oscillation criteria that extend and refine previous results. Illustrative examples are provided to validate the theoretical findings and highlight the effectiveness of the proposed methods. Full article

(This article belongs to the Section Mathematics)

18 pages, 1047 KiB

Open AccessArticle

Influence of the Effective Mass on the Properties of Nuclear Matter at Finite Density and Temperature

by Hajime Togashi, Debashree Sen, Hana Gil and Chang Ho Hyun

Symmetry 2025, 17(3), 445; https://doi.org/10.3390/sym17030445 - 17 Mar 2025

Viewed by 186

Abstract

The significance of the chiral symmetry restoration is studied by considering the role of the modification of the nucleon mass in nuclear medium at finite density and temperature. Using the Korea-IBS-Daegu-SKKU density functional theory, we can create models that have an identical nuclear [...] Read more.

The significance of the chiral symmetry restoration is studied by considering the role of the modification of the nucleon mass in nuclear medium at finite density and temperature. Using the Korea-IBS-Daegu-SKKU density functional theory, we can create models that have an identical nuclear matter equation of state but different isoscalar and isovector effective masses at zero temperature. The effect of the effective mass becomes transparent at non-zero temperatures, and it becomes more important as temperature increases. The role of the effective mass is examined thoroughly by calculating the dependence of thermodynamic variables such as free energy, internal energy, entropy, pressure and chemical potential on density, temperature and proton fraction. We find that sensitivity to the isoscalar effective mass is several times larger than that of the isovector effective mass, so the uncertainties arising from the effective mass are dominated by the isoscalar effective mass. In the analysis of the relative uncertainty, we obtain that the maximum uncertainty is less than 2% for free energy, internal energy and chemical potential, but it amounts to 20% for pressure. Entropy shows a behavior completely different from the other four variables that the uncertainty is about 40% at the saturation density and increases monotonically as density increases. The effect of the uncertainty to properties of physical systems is investigated with the proto-neutron star. It is shown that temperature depends strongly on the effective mass at a given density, and substantial swelling of the radius occurs due to the finite temperature. The equation of state is stiffer with smaller isoscalar effective mass, so the effect of the effective mass appears clearly in the mass–radius relation of the proto-neutron star, where a larger radius corresponds to a smaller effective mass. Full article

(This article belongs to the Special Issue Chiral Symmetry, and Restoration in Nuclear Dense Matter)

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21 pages, 1868 KiB

Open AccessArticle

Studies on Rhodanine Derivatives for Estimation of Chemical Reactivity Parameters by DFT

by Eleonora-Mihaela Ungureanu, Cornelia Elena Musina (Borsaru), Ovidiu-Teodor Matica, Raluca Isopescu, Gabriela Stanciu and Amalia Stefaniu

Symmetry 2025, 17(3), 444; https://doi.org/10.3390/sym17030444 - 16 Mar 2025

Viewed by 423

Abstract

Chemically modified electrodes based on derivatives of 2-thioxothiazolidin-4-one were mentioned as possible solutions for heavy metal (HM) ions heterogeneous recognition. Such ligands form thin films with reversible responses in the ferrocene redox probe with a well-defined symmetrical peak and symmetrical values for the [...] Read more.

Chemically modified electrodes based on derivatives of 2-thioxothiazolidin-4-one were mentioned as possible solutions for heavy metal (HM) ions heterogeneous recognition. Such ligands form thin films with reversible responses in the ferrocene redox probe with a well-defined symmetrical peak and symmetrical values for the anodic and cathodic currents. Their selectivity in coordinating HM ions was proven. In this paper, a computer-added study was performed using density functional theory (DFT) based on two methods, B3LYP and ωB97XD, to arrive at a better inside of their structure. Properties related to their reactivity concerning experimental electrochemical behaviour and spectral results were calculated using specific molecular descriptors. DFT-calculated HOMO-LUMO energies were found in good linear correlation with experimental redox potential. The accuracy of the calculations was also proven by a good agreement between the energy calculated by the DFT method and the UV-Vis spectra for the studied ligands. Such a computational approach can be used to evaluate the properties of possible new ligands for such electrochemical applications. The strong correlation between DFT-predicted quantum parameters and experimental redox potentials underscores the relevance of these computational approaches in designing selective molecular sensors. The results obtained using the two functionals are in good agreement, although there are also situations and parameters for which the results are not identical. There is a symmetry of the values obtained by the electrochemical and spectral methods with those calculated by DFT. Full article

(This article belongs to the Section Chemistry: Symmetry/Asymmetry)

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