Symmetry doi: 10.3390/sym16101376

Authors: Yanling Li Qianxing Sun Junfang Wei Chunyan Huang

Solving shallow water equations is crucial in science and engineering for understanding and predicting natural phenomena. To address the limitations of Physics-Informed Neural Network (PINN) in solving shallow water equations, we propose an improved PINN algorithm integrated with a deep learning framework. This algorithm introduces a regularization term as a penalty in the loss function, based on the PINN and Long Short-Term Memory (LSTM) models, and incorporates an attention mechanism to solve the original equation across the entire domain. Simulation experiments were conducted on one-dimensional and two-dimensional shallow water equations. The results indicate that, compared to the classical PINN algorithm, the improved algorithm shows significant advantages in handling discontinuities, such as sparse waves, in one-dimensional problems. It accurately captures sparse waves and avoids smoothing effects. In two-dimensional problems, the improved algorithm demonstrates good symmetry and effectively reduces non-physical oscillations. It also shows significant advantages in capturing details and handling complex phenomena, offering higher reliability and accuracy. The improved PINNs algorithm, which combines neural networks with physical mechanisms, can provide robust solutions and effectively avoid some of the shortcomings of classical PINNs methods. It also possesses high resolution and strong generalization capabilities, enabling accurate predictions at any given moment.

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Authors: Pucha Song Jinghua Ye Kang Yan Zhengyan Luo

Using adaptive filtering to estimate the frequency of power systems has become a popular trend. In recent years, however, few studies have been performed on adaptive frequency estimations in non-stationary noise environments. In this paper, we propose the distributed complex inverse square root algorithm and distributed augmented complex inverse square root algorithm for the frequency estimation of power systems based on the widely linear model and the inverse square root cost function, where the function can restrain both positive and negative large errors, based on its symmetry. Moreover, the wireless sensor networks support monitoring and adaptation for the frequency estimation in the distributed networks, and the proposed approach can ensure good robustness of the balanced or unbalanced three-phase power system with the help of a local complex-value voltage signal generated by Clark&rsquo;s transformation. In addition, the bound of step size is driven by the global vectors, and that low computation complexity do not hinder those performances. The results of several experiments demonstrate that our algorithms can effectively estimate the frequency in impulsive noise environments.

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Authors: Aguda E. Vincent George A. Tsirogiannis Angela E. Perdiou Vassilis S. Kalantonis

This paper investigates the movement of a negligible mass body (third body) in the vicinity of the out-of-plane equilibrium points of the Hill three-body problem under the effect of radiation pressure of the primaries. We study the effect of the radiation parameters through the factors qi,i=1,2 on the existence, position, zero-velocity curves and stability of the out-of-plane equilibrium points. These equilibrium positions are derived analytically under the action of radiation pressure exerted by the radiating primary bodies. We determined that these points emerge in symmetrical pairs, and based on the values of the radiation parameters, there may be two along the Oz axis and either none or two on the Oxz plane (outside the axes). A thorough numerical investigation found that both radiation factors have a strong influence on the position of the out-of-plane equilibrium points. Our results also reveal that the parameters have impact on the geometry of the zero-velocity curves. Furthermore, the stability of these points is examined in the linear sense. To do so, the spatial distribution of the eigenvalues on the complex plane of the linearized system is visualized for a wide range of radiation parameter combinations. By a numerical investigation, it is found that all equilibrium points are unstable in general.

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Authors: Vipavee Damminsed Rabian Wangkeeree

Nowadays, unlabeled data are abundant, while supervised learning struggles with this challenge as it relies solely on labeled data, which are costly and time-consuming to acquire. Additionally, real-world data often suffer from label noise, which degrades the performance of supervised models. Semi-supervised learning addresses these issues by using both labeled and unlabeled data. This study extends the twin support vector machine with the generalized pinball loss function (GPin-TSVM) into a semi-supervised framework by incorporating graph-based methods. The assumption is that connected data points should share similar labels, with mechanisms to handle noisy labels. Laplacian regularization ensures uniform information spread across the graph, promoting a balanced label assignment. By leveraging the Laplacian term, two quadratic programming problems are formulated, resulting in LapGPin-TSVM. Our proposed model reduces the impact of noise and improves classification accuracy. Experimental results on UCI benchmarks and image classification demonstrate its effectiveness. Furthermore, in addition to accuracy, performance is also measured using the Matthews Correlation Coefficient (MCC) score, and the experiments are analyzed through statistical methods.

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Authors: Chengmao Wu Siyu Zhou

Considering the shortcomings of Ruspini partition-based fuzzy clustering in revealing the intrinsic correlation between different classes, a series of harmonic fuzzy local information C-means clustering for noisy image segmentation are proposed. Firstly, aiming at the shortage of Zadeh&rsquo;s fuzzy sets, a new concept of generalized harmonic fuzzy sets is originally introduced and the corresponding harmonic fuzzy partition is further defined. Then, based on the concept of symmetric harmonic partition, a new harmonic fuzzy local information C-means clustering (HLICM) is proposed and the local convergence of the algorithm is rigorously proved using Zangwill&rsquo;s theorem. Finally, inspired by the improved fuzzy local information C-means clustering (IFLICM) and kernel-based weighted fuzzy local information C-means clustering (KWFLICM), two enhanced robust HLICM algorithms are constructed to further improve the ability of the algorithm to suppress noise. Compared with existing state-of-the-art robust fuzzy clustering-related algorithms, it has been confirmed that the two proposed algorithms have significant competitiveness and superiority.

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Authors: Anshui Li Jiajia Wang Lianlian Zhou

Uncertain differential equations, as an alternative to stochastic differential equations, have proved to be extremely powerful across various fields, especially in finance theory. The issue of parameter estimation for uncertain differential equations is the key step in mathematical modeling and simulation, which is very difficult, especially when the corresponding terms are driven by some complicated uncertain processes. In this paper, we propose the uncertainty counterpart of the threshold Ornstein&ndash;Uhlenbeck process in probability, named the uncertain threshold Ornstein&ndash;Uhlenbeck process, filling the gaps of the corresponding research in uncertainty theory. We then explore the parameter estimation problem under different scenarios, including cases where certain parameters are known in advance while others remain unknown. Numerical examples are provided to illustrate our method proposed. We also apply the method to study the term structure of the U.S. Treasury rates over a specific period, which can be modeled by the uncertain threshold Ornstein&ndash;Uhlenbeck process mentioned in this paper. The paper concludes with brief remarks and possible future directions.

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Authors: Maro Cvitan Predrag Dominis Prester Stefano Gregorio Giaccari Mateo Paulišić Ivan Vuković

The Moyal-Higher-Spin (MHS) formalism, involving fields dependent on spacetime and auxiliary coordinates, is an approach to studying higher-spin (HS)-like models. To determine the particle content of the MHS model of the Yang&ndash;Mills type, we calculate the quartic Casimir operator for on-shell MHS fields, finding it to be generally non-vanishing, indicative of infinite/continuous spin degrees of freedom. We propose an on-shell basis for these infinite/continuous spin states. Additionally, we analyse the content of a massive MHS model.

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Authors: Ohgi Takahashi

Succinimide residues formed spontaneously from aspartic acid (Asp) and asparagine (Asn) residues in proteins and peptides are stereochemically unstable, undergoing partial l-to-d stereoinversion, and this is responsible for the d-Asp and d-&beta;-Asp residues found in long-lived proteins. These stereoinverted abnormal amino acid residues are believed to be related to aging and some age-related diseases such as cataracts. Although the succinimide stereoinversion is nonenzymatic, a catalyst is required for it to occur at physiological temperature. In this study, it was found by density functional theory (DFT) calculations that a hydrogen phosphate ion (HPO42&minus;) can effectively catalyze the stereoinversion of the succinimide intermediate. The HPO42&minus; ion abstracts a proton from the asymmetric carbon atom of the succinimide residue to form an enolate intermediate. Then, while the resultant dihydrogen phosphate ion (H2PO4&minus;) remains bound to the enolate ion, a water molecule donates a proton to the enolate intermediate on the opposite side from the phosphate (which is the rate-determining step) to produce the inverted carbon atom. The calculated activation barrier (ca. 90 kJ mol&minus;1) is consistent with a slow in vivo reaction. The present found mechanism can be termed the &ldquo;unsymmetrical SE1&rdquo; or &ldquo;pseudo-SE2&rdquo; mechanism.

]]>Symmetry doi: 10.3390/sym16101368

Authors: Shrideh Al-Omari Wael Salameh Sharifah Alhazmi

The aim of this work is to examine some q-analogs and differential properties of the gamma integral operator and its convolution products. The q-gamma integral operator is introduced in two versions in order to derive pertinent conclusions regarding the q-exponential functions. Also, new findings on the q-trigonometric, q-sine, and q-cosine functions are extracted. In addition, novel results for first and second-order q-differential operators are established and extended to Heaviside unit step functions. Lastly, three crucial convolution products and extensive convolution theorems for the q-analogs are also provided.

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Authors: Meshayil M. Alsolmi Fatimah A. Almulhim Meraou Mohammed Amine Hassan M. Aljohani Amani Alrumayh Fateh Belouadah

This article defines a new distribution using a novel alpha power-transformed method extension. The model obtained has three parameters and is quite effective in modeling skewed, complex, symmetric, and asymmetric datasets. The new approach has one additional parameter for the model. Certain distributional and mathematical properties are investigated, notably reliability, quartile, moments, skewness, kurtosis, and order statistics, and several approaches of estimation, notably the maximum likelihood, least square, weighted least square, maximum product spacing, Cramer-Von Mises, and Anderson Darling estimators of the model parameters were obtained. A Monte Carlo simulation study was conducted to evaluate the performance of the proposed techniques of estimation of the model parameters. The actuarial measures are computed for our recommended model. At the end of the paper, two insurance applications are illustrated to check the potential and utility of the suggested distribution. Evaluation using four selection criteria indicates that our recommended model is the most appropriate probability model for modeling insurance datasets.

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Authors: Andrzej Katrusiak Hien Quy Le

Quaternion and biquaternion symmetry transformations have been applied to non-Cartesian reference systems of direct and reciprocal crystal lattices. The transformations performed directly in the sets of crystal reference axes simplify the calculations, eliminate the need for orthogonalization, permit the use of crystallographic vectors for defining the directions of rotations and perform the computations directly in the crystal coordinates. The applications of the general quaternion transformations are envisioned for physical, chemical, crystallographic and engineering applications. The general quaternion multiplication rules for any symmetry-unrestricted lattices have been derived for the triclinic crystallographic system and have been applied to the biquaternion representations of all point-group symmetry elements, including the crystallographic hexagonal system. Cayley multiplication matrices for point-groups, based on the biquaternion symbols of proper and improper symmetry elements, have been exemplified.

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Authors: Ayed. R. A. Alanzi Shokrya S. Alshqaq Raouf Fakhfakh

Several authors are interested in the study of limiting distributions for large symmetrical random matrices. Our approach of studying limiting distributions is different and is related to the new concept of variance functions of Cauchy&ndash;Stieltjes Kernel (CSK) families of probabilities. By means of the variance functions machinery, some novel limiting probability measures are provided involving the free multiplicative law of large numbers, using both free and Boolean (additive and multiplicative) convolutions. Several examples of these limiting probability measures are given in the context of free probability.

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Authors: Isyaku Muhammad Mustapha Muhammad Baohua Wang Wang Chen Badamasi Abba Mustapha Mukhtar Usman

The degradation of products is an integral part of their life-cycle, often following predictable trajectories. However, sudden, unexpected events, termed &rsquo;shocks&rsquo;, can substantially alter these degradation paths. Shocks can significantly influence the pace of degradation, leading to accelerated system failure. Moreover, they may initiate changes in degradation patterns, transitioning from linear to non-linear or random trajectories. To address this challenge, we present a novel multi-state reliability model for competing failure processes that account for degradation-shock dependencies by considering the state-varying degradation pattern. The degradation process is divided into s-states, with each state treated according to its pattern based on the time-transform Wiener process. The reliability function is derived based on soft failure caused by continuous degradation involving the s-states, the sudden increase in degradation caused by random shocks, and hard failure due to some shock processes. Additionally, we performed a sensitivity analysis to determine which parameters have the most significant impact on product reliability. Due to the complexity of the likelihood function, we adopted the ABC method to estimate the model parameters. A simulation study and a practical application with micro-electro-mechanical systems (MEMS) degradation results are used to demonstrate the efficiency and effectiveness of the proposed approach.

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Authors: Kun Yan Luyi Yang Zhanpeng Yang Wenjuan Ren

Deep neural network models are vulnerable to attacks from adversarial methods, such as gradient attacks. Evening small perturbations can cause significant differences in their predictions. Adversarial training (AT) aims to improve the model&rsquo;s adversarial robustness against gradient attacks by generating adversarial samples and optimizing the adversarial training objective function of the model. Existing methods mainly focus on improving robust accuracy, balancing natural and robust accuracy and suppressing robust overfitting. They rarely consider the AT problem from the characteristics of deep neural networks themselves, such as the stability properties under certain conditions. From a mathematical perspective, deep neural networks with stable training processes may have a better ability to suppress overfitting, as their training process is smoother and avoids sudden drops in performance. We provide a proof of the existence of Ulam stability for deep neural networks. Ulam stability not only determines the existence of the solution for an operator inequality, but it also provides an error bound between the exact and approximate solutions. The feature subspace of a deep neural network with Ulam stability can be accurately characterized and constrained by a function with special properties and a controlled error boundary constant. This restricted feature subspace leads to a more stable training process. Based on these properties, we propose an adversarial training framework called Ulam stability adversarial training (US-AT). This framework can incorporate different Ulam stability conditions and benchmark AT models, optimize the construction of the optimal feature subspace, and consistently improve the model&rsquo;s robustness and training stability. US-AT is simple and easy to use, and it can be easily integrated with existing multi-class AT models, such as GradAlign and TRADES. Experimental results show that US-AT methods can consistently improve the robust accuracy and training stability of benchmark models.

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Authors: Sahar Mohammad Abusalim Raouf Fakhfakh Fatimah Alshahrani Abdellatif Ben Makhlouf

Symmetrical fractional differential equations have been explored through a variety of methods in recent years. In this paper, we analyze the existence and uniqueness of a class of pantograph integro-fractional stochastic differential equations (PIFSDEs) using the Banach fixed-point theorem (BFPT). Also, Gronwall inequality is used to demonstrate the Ulam&ndash;Hyers stability (UHS) of PIFSDEs. The results are illustrated by two examples.

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Authors: Ştefan-Cezar Broscăţeanu Adela Mihai Andreea Olteanu

Both notions, of an infinitesimal bending of a curve and of a rectifying curve, play important roles in the theory of curves. In this short note, we begin the study of the infinitesimal bending of a rectifying curve.

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Authors: Ioannis Diamantis Sofia Lambropoulou Sonia Mahmoudi

In this paper, we extend the theory of planar pseudo knots to the theories of annular and toroidal pseudo knots. Pseudo knots are defined as equivalence classes under Reidemeister-like moves of knot diagrams characterized by crossings with undefined over/under information. In the theories of annular and toroidal pseudo knots, we introduce their respective lifts to the solid and the thickened torus. Then, we interlink these theories by representing annular and toroidal pseudo knots as planar O-mixed and H-mixed pseudo links. We also explore the inclusion relations between planar, annular and toroidal pseudo knots, as well as of O-mixed and H-mixed pseudo links. Finally, we extend the planar weighted resolution set to annular and toroidal pseudo knots, defining new invariants for classifying pseudo knots and links in the solid and in the thickened torus.

]]>Symmetry doi: 10.3390/sym16101359

Authors: Lei Shi Qing-Wen Wang Lv-Ming Xie Xiao-Feng Zhang

Dual generalized commutative quaternions have broad application prospects in many fields. Additionally, the matrix equation AXB=C has important applications in mathematics and engineering, especially in control systems, economics, computer science, and other disciplines. However, research on the matrix equation AXB=C over the dual generalized commutative quaternions remains relatively insufficient. In this paper, we derive the necessary and sufficient conditions for the solvability of the dual generalized commutative quaternion matrix equation AXB=C. Furthermore, we provide the general solution expression for this matrix equation, when it is solvable. Finally, a numerical algorithm and an example are provided to confirm the reliability of the main conclusions.

]]>Symmetry doi: 10.3390/sym16101358

Authors: Mintae Kim Oya Mert Coskun Seyma Ordu Resat Mutlu

The conformal fractional derivative (CFD) has become a hot research topic since it has a physical interpretation and is easier to grasp and apply to problems compared with other fractional derivatives. Its application to heat transfer, diffusion, diffusion-advection, and wave propagation problems can be found in the literature. Fractional diffusion equations have received great attention recently due to their applicability in physical, chemical, and biological processes and engineering. The diffusion of the pollutants within the ground, which is an important environmental problem, can be modeled with a diffusion equation. Diffusion in some porous materials or soil can be modeled more accurately with fractional derivatives or the conformal fractional derivative. In this study, the diffusion problem of a spilled pollutant leaking into the ground modeled with the conformal fractional time derivative in spherical coordinates has been solved analytically using the Fourier series for a constant mass flow rate and complete symmetry under the assumptions of homogeneous and isotropic soil, constant soil temperature, and constant permeability. The solutions have been simulated spatially and in time. A parametric analysis of the problem has been performed for several values of the CFD order. The simulation results are interpreted. It has also been suggested how to find the parameters of the soil to see whether the CFD can be used to model the soil or not. The approach described here can also be used for modeling pollution problems involving different boundary conditions.

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Authors: Lei Wang Xiaobo Li Shihao Yuan Feng Qian Zhangli Kang Shibin Li

NiOx, prepared via the sputtering method, exhibits low conductivity and energy level mismatch with the perovskite layer, thereby limiting further enhancements in the performance of perovskite solar modules (PSMs). Unlike traditional methods that enhance the performance of NiOx through reactive sputtering or directly doping NiOx targets with metal ions, both of which incur high costs and low efficiency, we employ an evaporation method using LiF to achieve efficient and low-cost doping of NiOx. Compared to the pristine NiOx, the incorporation of LiF significantly increases the conductivity of NiOx. Additionally, the incorporation of LiF enhances the quality of the deposited perovskite films, as well as the energy level alignment and symmetry between NiOx and the perovskite, effectively improving the hole extraction and transport capabilities between NiOx and the perovskite. As a result, the PSM (active area of 57.30 cm&sup2;) fabricated in air achieves an impressive efficiency of 19.54%. Furthermore, the unencapsulated PSM retains 80% of its initial efficiency after 700 h of continuous illumination, whereas the NiOx-based PSM drops to 80% after only 150 h. This study provides a simple and low-cost method for doping NiOx, which is of great significance for the further industrialization of PSMs.

]]>Symmetry doi: 10.3390/sym16101356

Authors: Jia Mao Yanzhi Zhou Yu Zhou Xi Wang

Background: Serious secondary disasters caused by extreme natural weather conditions occur frequently, making it essential to establish a scientific and efficient modern emergency management system to maximize life-saving efforts. Methods: This study focuses on the uncertain environment of urban road networks and employs fuzzy theory to construct a 0&ndash;1 integer programming model for emergency evacuation paths that minimizes the average expected travel time. Results: We enhanced the neighborhood search strategy of the traditional ACO_time by incorporating the 2-opt and 3-opt perturbation mechanisms from the SA algorithm. Additionally, we utilized improved ant-volume and ant-perimeter models, along with their combinations, in the pheromone-updating mechanism of the basic ACO. The heuristic principles of the A* algorithm were integrated, introducing the joint influence of path and time into the heuristic function of the ACO algorithm. Conclusions: The IACO3 algorithm was tested on the Sioux Falls network and the Berlin Heisenheimer Center network. The computation time of the improved IACO3 algorithm was reduced by up to 20% compared to the original IACO3 algorithm in relation to the SA algorithm, with only a 4&ndash;5% increase in computation time compared to the ACO_time algorithm, which translates to an increase of merely 4&ndash;5 s. This demonstrates the superior solution efficiency of the IACO3 algorithm.

]]>Symmetry doi: 10.3390/sym16101355

Authors: Hang Qi Ruiyang Su Runjia Sun Jiongcheng Yan

A rapid dynamic security assessment (DSA) is crucial for online preventive and restoration decision-making. The deep learning-based DSA models have high efficiency and accuracy. However, the complex model structure and high training cost make them hard to update quickly. This paper proposes a dynamic security partition assessment method, aiming to develop accurate and incrementally updated DSA models with simple structures. Firstly, the power grid is self-adaptively partitioned into several local regions based on the mean shift algorithm. The input of the mean shift algorithm is a symmetric electrical distance matrix, and the distance metric is the Chebyshev distance. Secondly, high-level features of operating conditions are extracted based on the stacked denoising autoencoder. The symmetric electrical distance matrix is modified to represent fault locations in local regions. Finally, DSA models are constructed for fault locations in each region based on the radial basis function neural network (RBFNN) and Chebyshev distance. An online incremental updating strategy is designed to enhance the model adaptability. With the simulation software PSS/E 33.4.0, the proposed dynamic security partition assessment method is verified in a simplified provincial system and a large-scale practical system in China. Test results demonstrate that the Chebyshev distance can improve the partition quality of the mean shift algorithm by approximately 50%. The RBFNN-based partition assessment model achieves an accuracy of 98.96%, which is higher than the unified assessment with complex models. The proposed incremental updating strategy achieves an accuracy of over 98% and shortens the updating time to 30 s, which can meet the efficiency of online application.

]]>Symmetry doi: 10.3390/sym16101354

Authors: Gabriel Hancu Adriana Modroiu Denisa Gabriela Stroia Alexandra Uilăcan

The current review provides a focused analysis of the application of capillary electrophoresis (CE) techniques to determine the chiral purity of pharmaceuticals, with a specific emphasis on cyclodextrin- (CD) based chiral selectors (CSs), highlighting advancements, methodologies, and trends in this area as reported in studies published from 2010 to 2024. The review emphasizes CE&rsquo;s evolution as a critical tool in this field, discussing its advantages, such as high efficiency, flexibility, relatively low costs, and minimal environmental impact, which make it well-suited for modern pharmaceutical applications. Additionally, it underscores the importance of CE in meeting stringent regulatory requirements for chiral drug substances. A significant shift in method optimization has occurred in the last ten years, shifting from the traditional One-Factor-at-a-Time (OFAT) strategy to the Design-of-Experiments (DoE) approach; this shift has enabled more systematic and robust method development. Furthermore, a common trend in recent years is the application of Quality-by-Design (QbD) principles in method development and optimization, ensuring higher reliability and efficiency. Additionally, there is an increasing focus on developing CE methods capable of detecting both achiral and chiral impurities simultaneously, which enhances the comprehensiveness of the analysis. This review seeks to guide future research and development in optimizing CE methodologies for pharmaceutical applications.

]]>Symmetry doi: 10.3390/sym16101353

Authors: Safaa Safouan Karim El Moutaouakil Alina-Mihaela Patriciu

The fuzzy C-means (FCM) clustering algorithm is a widely used unsupervised learning method known for its ability to identify natural groupings within datasets. While effective in many cases, FCM faces challenges such as sensitivity to initial cluster assignments, slow convergence, and difficulty in handling non-linear and overlapping clusters. Aimed at these limitations, this paper introduces a novel fractional fuzzy C-means (Frac-FCM) algorithm, which incorporates fractional derivatives into the FCM framework. By capturing non-local dependencies and long memory effects, fractional derivatives offer a more flexible and precise representation of data relationships, making the method more suitable for complex datasets. Additionally, a genetic algorithm (GA) is employed to optimize a new least-squares objective function that emphasizes the geometric properties of clusters, particularly focusing on the Fukuyama&ndash;Sugeno and Xie&ndash;Beni indices, thereby enhancing the balance between cluster compactness and separation. Furthermore, the Frac-FCM algorithm is evaluated on several benchmark datasets, including Iris, Seed, and Statlog, and compared against traditional methods like K-means, SOM, GMM, and FCM. The results indicate that Frac-FCM consistently outperforms these methods in terms of the Silhouette and Dunn indices. For instance, Frac-FCM achieves higher Silhouette scores of most cases, indicating more distinct and well-separated clusters. Dunn&rsquo;s index further shows that Frac-FCM generates clusters that are better separated, surpassing the performance of traditional methods. These findings highlight the robustness and superior clustering performance of Frac-FCM. The Friedman test was employed to enhance and validate the effectiveness of Frac-FCM.

]]>Symmetry doi: 10.3390/sym16101351

Authors: Jiwen Zhang Xingxing Huang Zhengwei Wang

The large dimensions of the 1000 MW hydroelectric generator sets require high mounting accuracy. Small deviations can lead to asymmetry, which in turn triggers unbalanced magnetic pulls and moments. Therefore, symmetry is a central challenge in the installation and operation of giant hydroelectric generators. In this paper, the effects of radial eccentricity, axial offset, and rotor shaft deflection on the unbalanced magnetic pull and moment are investigated by transient finite element analysis of the asymmetric magnetic field. The results of the time-domain and frequency-domain analyses show that asymmetric operation generates unbalanced magnetic forces and moments. These forces and moments increase linearly with increasing offset or deflection rate. When the eccentricity meets the installation criteria, the unbalanced magnetic pull forces are small and within acceptable limits. This study helps to understand the relationship between asymmetry and unbalanced magnetic pulling forces in large hydroelectric generators, and provides a theoretical basis for standardizing installation deviation control.

]]>Symmetry doi: 10.3390/sym16101352

Authors: Jawad Ali Suhad Ali Osman Abdallah N. S. Abd EL-Gawaad

The present study introduces an innovative approach to multi-criteria decision making (MCDM) aimed at handling decision analysis involving p,qrung orthopair fuzzy (p,qROF) data, where the criteria weights are completely unknown. To achieve this objective, we formulate generalized operational rules referred to as Frank operational rules, tailored for p,qROF numbers (p,qROFNs) utilizing the Frank t-norm and t-conorm. With these newly devised operations as a foundation, we create a variety of p,qROF aggregation operators (AOs) to effectively aggregate p,qROF information. Furthermore, we examine specific instances of these operators and rigorously establish their desirable properties, including idempotency, monotonicity, boundedness, and symmetry. Subsequently, we adapt the SWARA technique to the realm of p,qROF fuzzy data and this adapted technique becomes instrumental in determining criteria weights within the proposed MCDM framework centered around proposed AOs. We furnish a descriptive example to exemplify the practicality of the developed approach. Lastly, the effectiveness and soundness of our approach are underscored through both parameter analysis and a comparative evaluation.

]]>Symmetry doi: 10.3390/sym16101350

Authors: Franco Rubio-López Obidio Rubio Ronald León Alexis Rodriguez Daniel Chucchucan

In this paper, the authors generalize the fractional curvature of plane curves introduced by Rubio et al. in 2023, to regular curves in the Euclidean space R3, and study the geometric properties of the curve using Caputo&rsquo;s fractional derivative. Furthermore, we introduce a new definition of fractional curvature and fractional mean curvature of a regular surface, using fractional principal curvatures; and prove that such concepts are invariant under isometries; i.e., they belong to the intrinsic geometry of the regular surface. Also, a geometric interpretation is given to Caputo&rsquo;s fractional derivative of algebraic polynomials.

]]>Symmetry doi: 10.3390/sym16101349

Authors: Haihua Wang Jie Zhao

Inspired by prior research on fractional calculus, we introduce new fractional integral and derivative operators: the (&rho;1,&rho;2,k1,k2,&phi;)-proportional integral and the (&rho;1,&rho;2,k1,k2,&phi;)-proportional Hilfer fractional derivative. Numerous previous studied fractional integrals and derivatives can be considered as particular instances of the novel operators introduced above. Some properties of the (&rho;1,&rho;2,k1,k2,&phi;)-proportional integral are discussed, including mapping properties, the generalized Laplace transform of the (&rho;1,&rho;2,k1,k2,&phi;)-proportional integral and (&rho;1,&rho;2,k1,k2,&phi;)-proportional Hilfer fractional derivative. The results obtained suggest that the most comprehensive formulation of this fractional calculus has been achieved. Under the guidance of the findings from earlier sections, we investigate the existence of mild solutions for the (&rho;1,&rho;2,k1,k2,&phi;)-proportional Hilfer fractional Cauchy problem. An illustrative example is provided to demonstrate the main results.

]]>Symmetry doi: 10.3390/sym16101348

Authors: Marek T. Malinowski

In this paper, delayed stochastic integral equations with an initial condition and a drift coefficient given as interval-valued mappings are considered. These equations have a certain symmetric form that distinguishes them from classical single-valued stochastic integral equations and has implications for the properties of the diameter of the values of the solutions of the equations. The main result of the paper is the theorem that there is a unique solution to the equation considered. It was obtained under the assumptions of continuity of the kernels and Lipschitz continuity of the drift and diffusion coefficients. The proof of the existence of the solution is carried out by the method of iterating successive approximations. The paper ends with theorems about the continuous dependence of the solution on the initial function, kernels and nonlinearities.

]]>Symmetry doi: 10.3390/sym16101347

Authors: Zheyi Wu Haolin Liu Lei Wang

A time-lock puzzle encapsulates a secret message such that the receiver needs to perform a sequential computation, which takes a specified amount of time, to recover the message. Time-lock puzzles can be used in various scenarios, such as sealed-bid auctions, fair contract signing, and so on. The time required to generate a time-lock puzzle and the time needed to solve it are asymmetric, making the verification of a time-lock puzzle crucial. Before solving the puzzle, the solver needs to verify the validity of the puzzle to avoid computing invalid time-lock puzzles. After the puzzle has been solved, it is essential for a third party to confirm the correctness of the solution. This paper proposes a framework for time-lock puzzles, providing both pre-verification and post-verification functionalities, and outlines the security requirements of this framework. Furthermore, we present a practical construction based on iterated squaring in the RSA group and analyze the security of the specific construction. Finally, we implement this construction in Python and demonstrate its efficiency in different settings when implemented in practice.

]]>Symmetry doi: 10.3390/sym16101346

Authors: Aleksandar Kemiveš Milan Ranđelović Lidija Barjaktarović Predrag Đikanović Milan Čabarkapa Dragan Ranđelović

The advancement of technology has led humanity into the era of the information society, where information drives progress and knowledge is the most valuable resource. This era involves vast amounts of data, from which stored knowledge should be effectively extracted for use. In this context, machine learning is a growing trend used to address various challenges across different fields of human activity. This paper proposes an ensemble model that leverages multiple machine learning algorithms to determine the key factors for successful foreign direct investment, which simultaneously enables the prediction of this process using data from the World Bank, covering 60 countries. This innovative model, which adds to scientific and research knowledge, employs two sets of methods&mdash;binary regression and feature selection&mdash;combined in a stacking ensemble using a classification algorithm as the combiner to enable asymmetric optimization. The proposed predictive ensemble model has been tested in a case study using a dataset compiled from World Bank data across countries worldwide. The model demonstrates better performance than each of the individual algorithms integrated into it, which are considered state-of-the-art in these methodologies. Additionally, the findings highlight three key factors for foreign direct investment from the dataset, leading to the development of an optimized prediction formula.

]]>Symmetry doi: 10.3390/sym16101345

Authors: Xiaojian Li Lianzhong Li

In this study, we focus on investigating a novel extended (3+1)-dimensional Kadomtsev&ndash;Petviashvili&ndash;Boussinesq-like (KPB-like) equation. Initially, we utilized the Lie symmetry method to determine the symmetry generator by considering the Lie invariance condition. Subsequently, by similar reduction, the equation becomes ordinary differential equations (ODEs). Exact analytical solutions were derived through the power series method, with a comprehensive proof of solution convergence. Employing the (G&prime;/G2)-expansion method enabled the identification of trigonometric, exponential, and rational solutions of the equation. Furthermore, we established the auto-B&auml;cklund transformation of the equation. Multiple-soliton solutions were identified by utilizing Hirota&rsquo;s bilinear method. The fundamental properties of these solutions were elucidated through graphical representations. Our results are of certain value to the interpretation of nonlinear problems.

]]>Symmetry doi: 10.3390/sym16101344

Authors: Hamdi Gassara Mehdi Tlija Lassaad Mchiri Abdellatif Ben Makhlouf

This study treats the problem of Finite Time Stability Analysis (FTSA) and Finite Time Feedback Control (FTFC), using a Linear Matrix Inequalities Approach (LMIA). It specifically focuses on Takagi&ndash;Sugeno fuzzy Time Delay Fractional-Order Systems (TDFOS) that include nonlinear perturbations and interval Time Varying Delays (ITVDs). We consider the case of the Caputo Tempered Fractional Derivative (CTFD), which generalizes the Caputo Fractional Derivative (CFD). Two main results are presented: a two-step procedure is provided, followed by a more relaxed single-step procedure. Two examples are presented to show the reduction in conservatism achieved by the proposed methods. The first is a numerical example, while the second involves the FTFC of an inverted pendulum, which exhibits both symmetrical dynamics for small angular displacements and asymmetrical dynamics for larger deviations.

]]>Symmetry doi: 10.3390/sym16101343

Authors: Zhixiang Li Wanqin Wu Xuewen Tan Qing Miao

This study investigates a symmetric fractional-order epidemic model with time delays and non-monotonic incidence rates, considering two viral strains. By confirming the existence, uniqueness, and boundedness of the system&rsquo;s solutions, the research ensures the model&rsquo;s well-posedness, guaranteeing its mathematical soundness and practical relevance. The study calculates and evaluates the equilibrium points and the basic reproduction numbers R01 and R02 to understand the dynamic behavior of the model under different parameter settings. Through the application of the Lyapunov method, the research examines the asymptotic global stability of the system, determining whether it will converge to a particular equilibrium state over time. Furthermore, Hopf bifurcation theory is employed to investigate potential periodic solutions and bifurcation scenarios, highlighting how the system might shift from stability to periodic oscillations under certain conditions. By utilizing the Adams-Bashforth-Moulton numerical simulation method, the theoretical results are validated, reinforcing the conclusions and demonstrating the model&rsquo;s applicability in real-world contexts. It emphasizes the importance of fractional-order models in addressing epidemiological issues related to time delays (&tau;), individual heterogeneity (m, k), and memory effects (&theta;), offering greater accuracy compared with traditional integer-order models. In summary, this research provides a theoretical foundation and practical insights, enhancing the understanding and management of epidemic dynamics through fractional-order epidemic models.

]]>Symmetry doi: 10.3390/sym16101342

Authors: Zikang Yan Peishun Liu Xuefang Wang Haojie Gao Xiaolong Ma Xintong Hu

The rich information and complex background of industrial images make it a challenging task to improve the high compression rate of images. Current learning-based image compression methods mostly use customized convolutional neural networks (CNNs), which find it difficult to cope with the complex production background of industrial images. This causes useful information to be lost in the abundance of irrelevant data, making it difficult to accurately extract important features during the feature extraction stage. To address this, a Multi-path Residual Asymmetric Convolutional Compression Network (MRACNN) is proposed. Firstly, a Multi-path Residual Asymmetric Convolution Block (MRACB) is introduced, which includes the Multi-path Residual Asymmetric Convolution Down-sampling Module for down-sampling in the encoder to extract key features, and the Mult-path Residual Asymmetric Convolution Up-sampling Module for up-sampling in the decoder to recover details and reconstruct the image. This feature transfer and information flow enables the better capture of image details and important information, thereby improving the quality and efficiency of image compression and decompression. Furthermore, a two-branch enhanced local attention mechanisms, and a channel-squeezing entropy model based on the compression-based enhanced local attention module is proposed to enhance the performance of the modeled compression. Extensive experimental evaluations demonstrate that the proposed method outperforms state-of-the-art techniques, achieves superior Rate&ndash;Distortion Performance, and excels in preserving local details.

]]>Symmetry doi: 10.3390/sym16101341

Authors: Ali A. Shukur Viet-Thanh Pham Victor Kamdoum Tamba Giuseppe Grassi

We present a hyperchaotic oscillator with two linear terms and seven nonlinear terms that displays special algebraic properties. Notably, the introduced oscillator features distinct equilibrium types: single-point, line, and spherical equilibria. The introduced oscillator exhibits attractive dynamics like hyperchaos with two wing attractors. To gain a better understanding, we provide the bifurcation and Lyapunov exponents. The Kolmogorov&ndash;Sinai entropy is applied to show the complexity of the oscillator. A microcontroller realization confirms the reliability of the oscillator. The proposed oscillator is successfully applied for RNG.

]]>Symmetry doi: 10.3390/sym16101340

Authors: Felix M. Lev

The purpose of this paper is to explain at the simplest possible level why finite mathematics based on a finite ring of characteristic p is more general (fundamental) than standard mathematics. The belief of most mathematicians and physicists that standard mathematics is the most fundamental arose for historical reasons. However, simple mathematical arguments show that standard mathematics (involving the concept of infinities) is a degenerate case of finite mathematics in the formal limit p&rarr;&infin;; standard mathematics arises from finite mathematics in the degenerate case when operations modulo a number are discarded. Quantum theory based on a finite ring of characteristic p is more general than standard quantum theory because the latter is a degenerate case of the former in the formal limit p&rarr;&infin;.

]]>Symmetry doi: 10.3390/sym16101339

Authors: Wei He Xiangxun Kong Liang Tang Wenli Chen Wei Hu Guanbin Chen

Controlling the ground settlement and building deformation triggered by shield tunnelling, particularly within water-rich strata, poses a significant engineering challenge. This study conducts a finite element (FE) analysis focusing on the ground settlement and deformation of adjacent structures (with a minimum distance of 2.6 m to the tunnel) due to earth pressure balance (EPB) shield tunnelling. The analysis incorporates the influence of groundwater through a 3D fluid&ndash;solid coupling model. This study assesses the effects of tunnelling on the behaviour of nearby buildings and introduces two mitigation strategies: the vertical partition method and the portal partition method. Their effectiveness is compared and evaluated. Our findings reveal that the deformation curves of the stratum and the building are influenced by the accumulation and dissipation of pore pressure. The vertical partition method reduced surface settlement by approximately 70%, while the portal partition method further minimized building deformation but required careful application to avoid issues like uplift. Both methods effectively mitigate the impacts of tunnel construction, with the portal partition method offering superior performance in terms of material use and cost efficiency. This research provides a scientific foundation and technical guidance for similar engineering endeavours, which is vital for ensuring the safety of metro tunnel construction and the stability of adjacent buildings.

]]>Symmetry doi: 10.3390/sym16101338

Authors: Rabha M. El-Ashwah Alaa Hassan El-Qadeem Gangadharan Murugusundaramoorthy Ibrahim S. Elshazly Borhen Halouani

This work examines subordination conclusions for a specific subclass of p-valent meromorphic functions on the punctured unit disc of the complex plane where the function has a pole of order p. A new linear operator is used to define the subclass that is being studied. Furthermore, we present several corollaries with intriguing specific situations of the results.

]]>Symmetry doi: 10.3390/sym16101337

Authors: Quan Miao Erping Sun Yan Xu

The nonlinear properties and photophysical dynamics of aluminum and zinc tetracarboxy-phthalocyanines (AlPc and ZnPc) were studied using pulse trains of a 532 nm wavelength, which contain 25 subpulses with a 100 ps width and 13 ns spacing. Considering its interaction with long-duration pulses, the energy structure of phthalocyanine could be substituted by a five-level pattern. The nonlinear transmissions of pulse trains in AlPc and ZnPc were simulated by means of equations about the population rate coupled with the paraxial field equation of two-dimensional space. The well-known Crank&ndash;Nicholson numerical method was applied to the theoretical simulation. The results demonstrate that both phthalocyanines are efficient as optical limiters. In its low-intensity region, AlPc shows a much better OL effect than ZnPc. But in the region with high intensity, their energy transmittances are nearly the same. The nonlinear transmission of a pulse is susceptible to the state lifetime and cross section of one-photon absorption. Tetracarboxy-phthalocyanines have advantageous photophysical properties for applications in nonlinear optical areas, such as nonlinear optical devices like optical limiters. Adding central metals such as Al and Zn to phthalocyanines could enhance their photodynamic properties, making them potential optical limiters and photosensitizers.

]]>Symmetry doi: 10.3390/sym16101336

Authors: Na Li Mingming Fan Xiaoyan Zeng Ming Yan

Previous studies have demonstrated that the surface curvature of cylindrical magnetic nonawires can induce fascinating dynamic magnetization properties. It was recently proposed that ferromagnetic nanotubes can be utilized as skyrmion guides, enabling the avoidance of the annihilation of skyrmions in the lateral boundaries as in flat thin-film strips. In this work, we demonstrate via micromagnetic simulation that multiple skyrmions can be stabilized in a cross-section of a ferromagnetic nanotube with interfacial Dzyaloshinskii&ndash;Moriya interaction (iDMI). When uniformly arranged, these skyrmions together can perform as a crystal lattice for spin waves (SWs) propagating in the nanotube. Our simulations show that the skyrmion lattice can contribute a chiral effect to the SW passing through, namely a circular polarization of the SW. The handedness of the polarization is found to be determined by the polarity of the skyrmions. A physical explanation of the observed effect is provided based on the exchange of angular momentum between SWs and skyrmions during the scattering process. Our results display more possibilities to exploit magnetic nanotubes as SW and skyrmion guide in the development of novel spintronic devices.

]]>Symmetry doi: 10.3390/sym16101335

Authors: Gilberto Gonzalez-Avalos Gerardo Ayala-Jaimes Noe Barrera Gallegos Aaron Padilla Garcia

Most electrical energy generation systems are based on synchronous generators; as a result, their analysis always provides interesting findings, especially if an approach different to those traditionally studied is used. Therefore, an approach involving the modeling and simulation of a synchronous generator connected to an infinite bus through a transmission line in a bond graph is proposed. The behavior of the synchronous generator is analyzed in four case studies of the transmission line: (1) a symmetrical transmission line, where the resistance and inductance of the three phases (a,b,c) are equal, which determine resistances and inductances in coordinates (d,q,0) as individual decoupled elements; (2) a symmetrical transmission line for the resistances and for non-symmetrical inductances in coordinates (a,b,c) that result in resistances that are individual decoupled elements and in a field of inductances in coordinates (d,q,0); (3) a non-symmetrical transmission line for resistances and for symmetrical inductances in coordinates (a,b,c) that produce a field of resistances and inductances as individual elements decoupled in coordinates (d,q,0); and (4) a non-symmetrical transmission line for resistances and inductances in coordinates (a,b,c) that determine resistances and inductance fields in coordinates (d,q,0). A junction structure based on a bond graph model that allows for obtaining the mathematical model of this electrical system is proposed. Due to the characteristics of a bond graph, model reduction can be carried out directly and easily. Therefore, reduced bond graph models for the four transmission line case studies are proposed, where the transmission line is seen as if it were inside the synchronous generator. In order to demonstrate that the models obtained are correct, simulation results using the 20-Sim software are shown. The simulation results determine that for a symmetrical transmission line, currents in the generator in the d and q axes are &minus;25.87 A and 0.1168 A, while in the case of a non-symmetrical transmission line, these currents are &minus;26.14 A and 0.0211 A, showing that for these current magnitudes, the generator is little affected due to the parameters of the generator and the line. However, for a high degree of non-symmetry of the resistances in phases a, b and c, it causes the generator to reach an unstable condition, which is shown in the last simulation of the paper.

]]>Symmetry doi: 10.3390/sym16101334

Authors: Qiuying Li Limeng Zhang Shuo Liu

For highly reliable software systems, it is expensive, time consuming, or even infeasible to perform reliability testing via a conventional software reliability demonstration testing (SRDT) plan. Moreover, in the traditional SRDT approach, the various characteristics of the software system or test sets are not considered when making the testing schemes. Some studies have focused on the effect of software testability on SRDT, but only limited situations were discussed, and many theoretical and practical problems have been left unresolved. In this paper, an extended study on the quantitative relation between test effectiveness (TE) and test effort for SRDT is proposed. Theoretical derivation is put forward by performing statistical analysis for the test suite according to TE. The combinations of all the cases of zero-failure and revealed nonzero failure, as well as discrete-type software and continuous-type software, are studied with the corresponding failure probability models constructed. That is, zero-failure and nonzero failure, as well as discrete-type software and continuous-type software, respectively, constitute the symmetry and asymmetry of SRDT. Finally, we illustrated all the models and performed applications on the Siemens program suite. The experimental results show that within the same limitation of requirements and confidence levels, this approach can effectively reduce the number of test cases and the test duration, i.e., accelerate the test process and improve the efficiency of the SRDT.

]]>Symmetry doi: 10.3390/sym16101333

Authors: Salvador Romaguera

The notions of modular b-metric and modular b-metric space were introduced by Ege and Alaca as natural generalizations of the well-known and featured concepts of modular metric and modular metric space presented and discussed by Chistyakov. In particular, they stated generalized forms of Banach&rsquo;s contraction principle for this new class of spaces thus initiating the study of the fixed point theory for these structures, where other authors have also made extensive contributions. In this paper we endow the modular b-metrics with a metrizable topology that supplies a firm endorsement of the idea of convergence proposed by Ege and Alaca in their article. Moreover, for a large class of modular b-metric spaces, we formulate this topology in terms of an explicitly defined b-metric, which extends both an important metrization theorem due to Chistyakov as well as the so-called topology of metric convergence. This approach allows us to characterize the completeness for this class of modular b-metric spaces that may be viewed as an offsetting of the celebrated Caristi&ndash;Kirk theorem to our context. We also include some examples that endorse our results.

]]>Symmetry doi: 10.3390/sym16101332

Authors: Daurenbek Serikbaev Niyaz Tokmagambetov

We examine a time-fractional pseudo-hyperbolic equation involving positive operators. We explore the determination of initial velocity and perturbation. It is demonstrated that these initial inverse problems are ill posed. Additionally, we prove that under certain conditions, the inverse problems exhibit well-posedness properties. Our focus is on developing a theoretical framework for these initial inverse problems associated with time-fractional pseudo-hyperbolic equations, laying the groundwork for future studies on numerical algorithms to solve these problems. This investigation is crucial for understanding the fundamental behavior of the equations under various initial conditions and perturbations. By establishing a rigorous theoretical framework, we pave the way for future research to focus on practical numerical methods and simulations. Our results provide a deeper insight into the mathematical structure of time-fractional pseudo-hyperbolic equations, ensuring that future computational approaches are built on a solid theoretical foundation.

]]>Symmetry doi: 10.3390/sym16101331

Authors: Simimole Haleema Chithra Gopinath Zabeera Kallingathodi Grace Thomas Prasad L. Polavarapu

Garcinia gummi-gutta, commonly known as Garcinia cambogia (syn.), is a popular traditional herbal medicine known for its role in treating obesity, and has been incorporated into several nutraceuticals globally for this purpose. The fruit rind is also used as a food preservative and a condiment because of its high content of hydroxycitric acid, which imparts a sharp, sour flavour. This review highlights the major bioactive compounds present in the tree Garcinia gummi-gutta, with particular emphasis on (2S, 3S)-tetrahydro-3-hydroxy-5-oxo-2,3-furan dicarboxylic acid, commonly referred to as garcinia acid. This acid can be isolated in large amounts through a simple procedure. Additionally, it explores the synthetic transformations of garcinia acid into biologically potent and functionally useful enantiopure compounds, a relatively under-documented area in the literature. This acid, with its six-carbon skeleton, a &gamma;-butyrolactone moiety, and two chiral centres bearing chemically amenable functional groups, offers a versatile framework as a chiron for the construction of diverse molecules of both natural and synthetic origin. The synthesis of chiral 3-substituted and 3,4-disubstituted pyrrolidine-2,5-diones, analogues of the Quararibea metabolite&mdash;a chiral enolic-&gamma;-lactone; the concave bislactone skeletons of fungal metabolites (+)-avenaciolide and (&minus;)-canadensolide; the structural skeletons of the furo[2,3-b]furanol part of the anti-HIV drug Darunavir; (&minus;)-tetrahydropyrrolo[2,1-a]isoquinolinones, an analogue of (&minus;)-crispine A; (&minus;)-hexahydroindolizino[8,7-b]indolones, an analogue of the naturally occurring (&minus;)-harmicine; and furo[2,3-b]pyrroles are presented here.

]]>Symmetry doi: 10.3390/sym16101330

Authors: Angela Bašić-Šiško Loredana Simčić Ivan Dražić

In this work, we analyze a spherically symmetric 3D flow of a micropolar, viscous, polytropic, and heat-conducting real gas. In particular, we take as a domain the subset of R3 bounded by two concentric spheres that present solid thermoinsulated walls. Also, here, we consider the generalized equation of state for the pressure in the sense that the pressure depends, as a power function, on the mass density. The model is based on the conservation laws for mass, momentum, momentum moment, and energy, as well as the equation of state for a real gas, and it is derived first in the Eulerian and then in the Lagrangian description. Through the application of the Faedo&ndash;Galerkin method, a numerical solution to a corresponding problem is obtained, and numerical simulations are performed to demonstrate the behavior of the solutions under various parameters and initial conditions in order to validate the method. The results of the simulations are discussed in detail.

]]>Symmetry doi: 10.3390/sym16101329

Authors: Ashraf ELrokh Rashad Ismail Atef Abd El-hay Yasser Elmshtaye

The journal Symmetry retracts the article titled &ldquo;On Cubic Roots Cordial Labeling for Some Graphs&rdquo; [...]

]]>Symmetry doi: 10.3390/sym16101328

Authors: Feifan Feng Yunjun Lu Weiwei Chen

In view of the high-sensitivity vibration effect of precision instrument laboratory buildings under the influence of surrounding traffic loads, field micro-vibration tests under various working conditions were carried out based on actual projects. Combined with numerical simulation, measured data served as input loads to simulate the vibration effect of various traffic loads on the floor of a building structure, and the structural vibration laws under the comprehensive action of various loads were analyzed. The vibration isolation effect of the isolation ditch on the oblique orthogonal load was investigated according to the corresponding safety index. The results show that the main frequency components of the site vibration frequency caused by various traffic loads are approximately 25 Hz and that the root-mean-square speed value is stable below VC-E, which meets the design requirements. Under the comprehensive action of multiple loads, the site structure will produce a vibration amplification effect, which is obvious when all types of loads are distributed symmetrically and the curve distribution is controlled by load factors with large amplitudes. The isolation effect of a small isolation ditch is best when it is located close to the source and the building. The depth of the isolation ditch must be greater than the maximum depth of the source to achieve better results, and the width has little influence. The effect of a small isolation trench on vertical vibration is poor, and the oblique orthogonal triaxial load has a counteracting effect on the vertical component. Thus, additional structural vibration isolation measures are needed. The research results provide a reference for engineering vibration isolation, damping measures, and structural design.

]]>Symmetry doi: 10.3390/sym16101327

Authors: Hongwu Qin Yanyan Han Xiuqin Ma

The interval-valued fuzzy soft set (IVFSS) model, which combines the benefits of the soft set model with the interval-valued fuzzy set (IVFS) model, is a growing and effective mathematical tool for processing hazy data. In detail, this model is characterized by symmetry, which has the lower and upper membership degree. The study of decision-making based on IVFSS has picked up more steam recently. However, existing multi-attribute decision-making (MADM) methods can only sort alternative schemes, but are not able to classify them, which is detrimental to decision-makers&rsquo; efficient decision-making. In this paper, we propose a multi-attribute three-way decision-making (MATWDM) algorithm based on ideal solutions for IVFSS. MATWDM is extended to the IVFSS environment by incorporating the concept of the ideal solution, offering a more adaptable and comprehensive approach for addressing uncertain MADM issues. The method not only obtains the ranking results of the alternatives, but also divides them into acceptance domain, rejection domain, and delayed-decision domain, which makes the decision results more reasonable and effective, facilitating decision-makers to make better decisions. We apply the proposed three-way decision algorithm to two practical cases as diverse as mine emergency decision and Homestay selection decision. Additionally, the effectiveness and viability of the suggested method are confirmed by experimental findings.

]]>Symmetry doi: 10.3390/sym16101326

Authors: Abdul Rahman S. Juma Nihad Hameed Shehab Daniel Breaz Luminiţa-Ioana Cotîrlă Maslina Darus Alin Danciu

This article aims to significantly advance geometric function theory by providing a valuable contribution to analytic and multivalent functions. It focuses on differential subordination and superordination, which characterize the interactions between analytic functions. To achieve our goal, we employ a method that relies on the characteristics of differential subordination and superordination. As one of the latest advancements in this field, this technique is able to derive several results about differential subordination and superordination for multivalent functions defined by the new operator M&lambda;,pmv,&rho;;&eta;F&xi; within the open unit disk A. Additionally, by employing the technique, the differential sandwich outcome is achieved. Therefore, this work presents crucial exceptional instances that follow the results. The findings of this paper can be applied to a wide range of mathematical and engineering problems, including system identification, orthogonal polynomials, fluid dynamics, signal processing, antenna technology, and approximation theory. Furthermore, this work significantly advances the knowledge and understanding of the analytical functions of the unit and its interactive higher relations. The characteristics and consequences of differential subordination theory are symmetric to those of differential superordination theory. By combining them, sandwich-type theorems can be derived.

]]>Symmetry doi: 10.3390/sym16101325

Authors: Aurélien Drezet

In this work, we analyze recent proposals by Das and D&uuml;rr (DD) to measure the arrival time distributions of quantum particles within the framework of de Broglie Bohm theory (or Bohmian mechanics). We also analyze the criticisms made by Goldstein Tumulka and Zangh&igrave; (GTZ) of these same proposals, and show that each protagonist is both right and wrong. In detail, we show that DD&rsquo;s predictions are indeed measurable in principle, but that they will not lead to violations of the no-signalling theorem used in Bell&rsquo;s theorem, in contradiction with some of Das and Maudlin&rsquo;s hopes.

]]>Symmetry doi: 10.3390/sym16101324

Authors: Yue Zeng Lu-Chuan Ceng Liu-Fang Zheng Xie Wang

Convex bilevel optimization problems (CBOPs) exhibit a vital impact on the decision-making process under the hierarchical setting when image restoration plays a key role in signal processing and computer vision. In this paper, a modified double inertial extragradient-like approach with a line search procedure is introduced to tackle the CBOP with constraints of the CFPP and VIP, where the CFPP and VIP represent a common fixed point problem and a variational inequality problem, respectively. The strong convergence analysis of the proposed algorithm is discussed under certain mild assumptions, where it constitutes both sections that possess a mutual symmetry structure to a certain extent. As an application, our proposed algorithm is exploited for treating the image restoration problem, i.e., the LASSO problem with the constraints of fractional programming and fixed-point problems. The illustrative instance highlights the specific advantages and potential infect of the our proposed algorithm over the existing algorithms in the literature, particularly in the domain of image restoration.

]]>Symmetry doi: 10.3390/sym16101323

Authors: Hussain Al-Qassem Mohammed Ali

This paper focuses on studying the mapping properties of singular integral operators over product symmetric spaces. The boundedness of such operators is established on Triebel&ndash;Lizorkin spaces whenever their rough kernel functions belong to the Grafakos and Stefanov class. Our findings generalize, extend and improve some previously known results on singular integral operators.

]]>Symmetry doi: 10.3390/sym16101322

Authors: Anthony Sofo

We investigate the linear arrangement of Euler harmonic sums that may be expressed in closed form in terms of special functions such as the classical Riemann zeta function and the Dirichlet eta function. Particular emphasis is given to Euler harmonic sums with even weight. New examples highlighting the theorems will be presented.

]]>Symmetry doi: 10.3390/sym16101321

Authors: Nikolay D. Dimitrov Jagan Mohan Jonnalagadda

In this paper, we examine a fourth-order equation that has parameter dependency and boundary conditions in three different places. We prove some of the features of the relevant asymmetric Green&rsquo;s function and infer its exact form. The resulting solutions are still positive and decreasing functions on the entire interval of the Green&rsquo;s function definition, and they are concave in a specific subinterval, despite the fact that the function&rsquo;s sign changes on the square of its definition. The fixed point theorem of Krasnoselskii is the foundation of the existence arguments. Next, using the Leggett&ndash;Williams fixed point theorem, it is concluded that there are at least three positive solutions. Lastly, an example is provided, to highlight the primary findings of the manuscript.

]]>Symmetry doi: 10.3390/sym16101320

Authors: Lorentz Jäntschi

Linear relationships, expressing the electrochemical properties of molecules as functions of structure, give insight into the associated electrochemical process and are a tool for prediction. Many biological activities rely on water-based dissociation, making electrochemical properties a bridge between structure and activity. Motivated by a previous study, a replica is made here on a different dataset in order to validate/invalidate the previously reported results. There are several methods for obtaining structure-based descriptors. Some of the methods have been devised to account for molecular topology, some to account for molecular geometry, and others to account for both. Two methods are involved here to derive structure-based descriptors and further obtain structure&ndash;property relationships (FMPI and ChPE). In order to express structure descriptors, both FMPI and ChPE express first the topology of the molecule, using the heavy atoms identity matrix and the heavy atoms adjacency matrix, both square symmetric matrices in the belief that symmetry is one major factor of molecular stability. A set of 2,6-dimethyl-1,4-dihydropyridine derivatives with oxidation peak potentials and coulometrically determined number of electrons experimental data is subjected to the search for structure&ndash;activity relationships. Even if the 2,6-dimethyl-1,4-dihydropyridine is a symmetric compound (of Cs point group), their derivatives are generally not symmetric (9 out of 24 are asymmetric). The dataset is subjected to descriptive and inferential statistics in order to filter out the most relevant structure&ndash;activity relationship. The geometry is built using three levels of theory (one from molecular mechanics and two others from density functionals, of which one accounts for the interaction with water as solvent). One challenge of picking one out of two reported measured values is dealt with by calculating the likelihood associated with the two choices. Relevant structure&ndash;activity models are extracted and discussed. The use of in vivo (in water, SM8 model) models in geometry optimization (from MMFF94 and B3LYP and to M06 + Water SM8) results in a precision gain, but this is, in most of the cases, not statistically significant, and this can be considered a negative result.

]]>Symmetry doi: 10.3390/sym16101319

Authors: Sanjay Kumar Amit Kumar Pooja Gupta Ram Pravesh Prasad Praveen Kumar

This research article introduces a novel chaotic satellite system based on fractional derivatives. The study explores the characteristics of various fractional derivative satellite systems through detailed phase portrait analysis and computational simulations, employing fractional calculus. We provide illustrations and tabulate the phase portraits of these satellite systems, highlighting the influence of different fractional derivative orders and parameter values. Notably, our findings reveal that chaos can occur even in systems with fewer than three dimensions. To validate our results, we utilize a range of analytical tools, including equilibrium point analysis, dissipative measures, Lyapunov exponents, and bifurcation diagrams. These methods confirm the presence of chaos and offer insights into the system&rsquo;s dynamic behavior. Additionally, we demonstrate effective control of chaotic dynamics using feedback active control techniques, providing practical solutions for managing chaos in satellite systems.

]]>Symmetry doi: 10.3390/sym16101318

Authors: Kamran Foroutan Farshid Torabi

This study utilizes a semi-analytical approach to examine the nonlinear dynamic responses of multilayer functionally graded (MFG) cylindrical shells reinforced by FG spiral stiffeners (FGSSs), which may have symmetric or asymmetric angles, under a thermal condition. It is presumed that the temperature is distributed across the thickness direction. The shell includes three layers: an outer ceramic-rich layer, a middle FG layer, and an inner metal-rich layer. By applying classical shell theory (CST), the smeared stiffeners technique, von K&aacute;rm&aacute;n equations, and the Galerkin method, the problem of nonlinear vibrations (NVs) has been addressed. Furthermore, the method of multiple scales (MMSs) is applied to investigate the nonlinear vibrational characteristics of the MFG cylindrical shells reinforced by FGSS, particularly focusing on the 1:2:4 internal resonance and the subharmonic resonance of order 1/2. This study finds that FG spiral stiffeners with symmetric or asymmetric angles and ambient temperature significantly affect the vibrational properties of the MFG cylindrical shells reinforced by spiral stiffeners.

]]>Symmetry doi: 10.3390/sym16101317

Authors: Sezer Erdem

In this article, the regular Schr&ouml;der&ndash;Catalan matrix is constructed and acquired by benefiting Schr&ouml;der and Catalan numbers. After that, two sequence spaces are introduced, described as the domain of Schr&ouml;der&ndash;Catalan matrix. Additionally, some algebraic and topological properties of the spaces in question, such as completeness, inclusion relations, basis and duals, are examined. In the last two sections, the necessary and sufficient conditions of some matrix classes and compact operators related aforementioned spaces are presented.

]]>Symmetry doi: 10.3390/sym16101316

Authors: Xiusong You Shirong Ge

To further enhance the intelligent construction of coal mines and improve the control accuracy of hydraulic support displacement straightness, a digital twin control method for hydraulic support displacement has been proposed. First, a dataset related to hydraulic support is established, and a ridge regression prediction model is developed to achieve digital twin-based displacement decision analysis. Next, by analyzing the mechanical structure and displacement principles of the hydraulic supports, a hydraulic cylinder mathematics model is established, leading to the state-space representation of the controlled object. This study focuses on error control during the multi-agent operation of the hydraulic supports, designing a corresponding controller and using discretization methods to verify the consistency of output displacement between followers and leaders. Finally, simulation experiments based on the digital twin model of hydraulic supports are conducted, validating that the hydraulic supports can be controlled in formation according to actual production requirements. The digital twin control method enables the precise adaptive displacement control of hydraulic supports and provides valuable insights for the intelligent construction of mining faces.

]]>Symmetry doi: 10.3390/sym16101315

Authors: Helton Saulo Roberto Vila Rubens Souza

This paper introduces bivariate log-symmetric models for analyzing the relationship between two variables, assuming a family of log-symmetric distributions. These models offer greater flexibility than the bivariate lognormal distribution, allowing for better representation of diverse distribution shapes and behaviors in the data. The log-symmetric distribution family is widely used in various scientific fields and includes distributions such as log-normal, log-Student-t, and log-Laplace, among others, providing several options for modeling different data types. However, there are few approaches to jointly model continuous positive and explanatory variables in regression analysis. Therefore, we propose a class of generalized linear model (GLM) regression models based on bivariate log-symmetric distributions, aiming to fill this gap. Furthermore, in the proposed model, covariates are used to describe its dispersion and correlation parameters. This study uses a dataset of anthropometric measurements of newborns to correlate them with various biological factors, proposing bivariate regression models to account for the relationships observed in the data. Such models are crucial for preventing and controlling public health issues.

]]>Symmetry doi: 10.3390/sym16101314

Authors: Shuanghua Luo Yu Zheng Cheng-yi Zhang

Under the assumption of missing response data, empirical likelihood inference is studied via composite quantile regression. Firstly, three empirical likelihood ratios of composite quantile regression are given and proved to be asymptotically &chi;2. Secondly, without an estimation of the asymptotic covariance, confidence intervals are constructed for the regression coefficients. Thirdly, three estimators are presented for the regression parameters to obtain its asymptotic distribution. The finite sample performance is assessed through simulation studies, and the symmetry confidence intervals of the parametric are constructed. Finally, the effectiveness of the proposed methods is illustrated by analyzing a real-world data set.

]]>Symmetry doi: 10.3390/sym16101313

Authors: Hua Luo Alhussein Mohamed

In this paper, we delve into a discrete nonlinear singular semipositone problem, characterized by a nonlinear boundary condition. The nonlinearity, given by f(u)&minus;au&alpha; with &alpha;&gt;0, exhibits a singularity at u=0 and tends towards &minus;&infin; as u approaches 0+. By constructing some suitable auxiliary problems, the difficulty that arises from the singularity and semipositone of nonlinearity and the lack of a maximum principle is overcome. Subsequently, employing the Krasnosel&rsquo;skii fixed-point theorem, we determine the parameter range that ensures the existence of at least one positive solution and the emergence of at least two positive solutions. Furthermore, based on our existence results, one can obtain the symmetry of the solutions after adding some symmetric conditions on the given functions by using a standard argument.

]]>Symmetry doi: 10.3390/sym16101312

Authors: Zhongxing Peng Gengzhong Zheng Wei Huang

In this paper, we introduce an efficient and effective algorithm for Graph-based Semi-Supervised Learning (GSSL). Unlike other GSSL methods, our proposed algorithm achieves efficiency by constructing a bipartite graph, which connects a small number of representative points to a large volume of raw data by capturing their underlying manifold structures. This bipartite graph, with a sparse and anti-diagonal affinity matrix which is symmetrical, serves as a low-rank approximation of the original graph. Consequently, our algorithm accelerates both the graph construction and label propagation steps. In particular, on the one hand, our algorithm computes the label propagation in closed-form, reducing its computational complexity from cubic to approximately linear with respect to the number of data points; on the other hand, our algorithm calculates the soft label matrix for unlabeled data using a closed-form solution, thereby gaining additional acceleration. Comprehensive experiments performed on six real-world datasets demonstrate the efficiency and effectiveness of our algorithm in comparison to five state-of-the-art algorithms.

]]>Symmetry doi: 10.3390/sym16101311

Authors: Dexian Wang Qilong Liu Jinghui Yang Delin Huang

Intelligent mobile robots have been gradually used in various fields, including logistics, healthcare, service, and maintenance. Path planning is a crucial aspect of intelligent mobile robot research, which aims to empower robots to create optimal trajectories within complex and dynamic environments autonomously. This study introduces an improved A* algorithm to address the challenges faced by the preliminary A* pathfinding algorithm, which include limited efficiency, inadequate robustness, and excessive node traversal. Firstly, the node storage structure is optimized using a minimum heap to decrease node traversal time. In addition, the heuristic function is improved by adding an adaptive weight function and a turn penalty function. The original 8-neighbor is expanded to a 16-neighbor within the search strategy, followed by the elimination of invalid search neighbor to refine it into a new 8-neighbor according to the principle of symmetry, thereby enhancing the directionality of the A* algorithm and improving search efficiency. Furthermore, a bidirectional search mechanism is implemented to further reduce search time. Finally, trajectory optimization is performed on the planned paths using path node elimination and cubic Bezier curves, which aligns the optimized paths more closely with the kinematic constraints of the robot derivable trajectories. In simulation experiments on grid maps of different sizes, it was demonstrated that the proposed improved A* algorithm outperforms the preliminary A* Algorithm in various metrics, such as search efficiency, node traversal count, path length, and inflection points. The improved algorithm provides substantial value for practical applications by efficiently planning optimal paths in complex environments and ensuring robot drivability.

]]>Symmetry doi: 10.3390/sym16101310

Authors: Fernando Haas

There are several versions of the damped form of the celebrated Pinney equation, which is the natural partner of the undamped time-dependent harmonic oscillator. In this work, these dissipative versions of the Pinney equation are briefly reviewed. We show that Noether&rsquo;s theorem for the usual time-dependent harmonic oscillator as a guiding principle for derivation of the Pinney equation also works in the damped case, selecting a Noether symmetry-based damped Pinney equation. The results are extended to general nonlinear damped Ermakov systems. A certain time-rescaling always allows to remove the damping from the final equations.

]]>Symmetry doi: 10.3390/sym16101309

Authors: Ping Zhao Yan Sun Zhanqi Wang Panpan Guo

The purpose of this paper is to capture the mechanical response of the support structure of deep excavation subject asymmetric load. A two-dimensional (2D) numerical analysis model was established by taking a pipe gallery deep excavation subject to asymmetric load as an example. The numerical analysis results were in good agreement with the measured data, thus verified the validity of the numerical model. On this basis, the stress and displacement of support structure caused by the change in foundation asymmetric load were studied. According to the numerical results, horizontal displacement of the diaphragm wall (DW) was dominant, and the maximum horizontal displacement of the DW was 7.54 mm when the deep excavation was completed. With the increase in asymmetric load, the left wall displacement continued to increase, while the displacement of the right DW continued to decrease, and the maximum horizontal wall displacement occurred near the excavation face. The DW was the main bending component, and the maximum wall bending moment when the deep excavation was completed was 173.5 kN&middot;m. The maximum wall bending moment increased with the increase in asymmetric load, and the maximum wall bending moment on the left of the deep excavation was greater than that on the right. The inner support sustained the main component of axial force, with the axial force peaking at 1051.8 kN when the deep excavation was completed. The axial force of the inner support increased with increasing the asymmetric load, and the axial force of the second inner support was obviously greater than that of the first inner support. This research has a positive effect on the design and optimization of deep excavation support structure subject to asymmetric load on ground surface.

]]>Symmetry doi: 10.3390/sym16101308

Authors: Sayantan Choudhury Suman Dey Rakshit Mandish Gharat Saptarshi Mandal Nilesh Pandey

In this work, we study the time-dependent behavior of quantum correlations of a system of an inverted oscillator governed by out-of-equilibrium dynamics using the well-known Schwinger&ndash;Keldysh formalism in the presence of quantum mechanical quench. Considering a generalized structure of a time-dependent Hamiltonian for an inverted oscillator system, we use the invariant operator method to obtain its eigenstate and continuous energy eigenvalues. Using the expression for the eigenstate, we further derive the most general expression for the generating function as well as the out-of-time-ordered correlators (OTOCs) for the given system using this formalism. Further, considering the time-dependent coupling and frequency of the quantum inverted oscillator characterized by quench parameters, we comment on the dynamical behavior, specifically the early, intermediate and late time-dependent features of the OTOC for the quenched quantum inverted oscillator. Next, we study a specific case, where the system of an inverted oscillator exhibits chaotic behavior by computing the quantum Lyapunov exponent from the time-dependent behavior of OTOCs in the presence of the given quench profile.

]]>Symmetry doi: 10.3390/sym16101307

Authors: Shrideh Al-Omari Wael Salameh

In this article, the (p,q)-analogs of the &alpha;-th fractional Fourier transform are provided, along with a discussion of their characteristics in specific classes of (p,q)-generalized functions. Two spaces of infinitely (p,q)-differentiable functions are defined by introducing two (p,q)-differential symmetric operators. The (p,q)-analogs of the &alpha;-th fractional Fourier transform are demonstrated to be continuous and linear between the spaces under discussion. Next, theorems pertaining to specific convolutions are established. This leads to the establishment of multiple symmetric identities, which in turn requires the construction of (p,q)-generalized spaces known as (p,q)-Boehmians. Finally, in addition to deriving the inversion formulas, the generalized (p,q)- analogs of the &alpha;-th fractional Fourier transform are introduced, and their general properties are discussed.

]]>Symmetry doi: 10.3390/sym16101306

Authors: Sayed Murad Ali Shah Yufeng Nie Anwarud Din Abdulwasea Alkhazzan

In this study, we explore the concept of symmetry as it applies to the dynamics of the Hepatitis B Virus (HBV) epidemic model. By incorporating symmetric principles in the stochastic model, we ensure that the control strategies derived are not only effective but also consistent across varying conditions, and ensure the reliability of our predictions. This paper presents a stochastic optimal control analysis of an HBV epidemic model, incorporating vaccination as a pivotal control measure. We formulate a stochastic model to capture the complex dynamics of HBV transmission and its progression to acute and chronic stages. By leveraging stochastic differential equations, we examine the model&rsquo;s stationary distribution and asymptotic behavior, elucidating the impact of random perturbations on disease dynamics. Optimal control theory is employed to derive control strategies aimed at minimizing the disease burden and vaccination costs. Through rigorous numerical simulations using the fourth-order Runge&ndash;Kutta method, we demonstrate the efficacy of the proposed control measures. Our findings highlight the critical role of vaccination in controlling HBV spread and provide insights into the optimization of vaccination strategies under stochastic conditions. The symmetry within the proposed model equations allows for a balanced approach to analyzing both acute and chronic stages of HBV.

]]>Symmetry doi: 10.3390/sym16101305

Authors: Yue Xiang Jingjing Guo Zhengyan Mao Chao Jiang Mandan Liu

This study presents a bi-objective optimization model for the Green Vehicle-Routing Problem in cold chain logistics, with a focus on symmetric distance matrices, aiming to minimize total costs, including carbon emissions, while maximizing customer satisfaction. To address this complex challenge, we developed a Stage-Specific Multi-Objective Five-Element Cycle Optimization algorithm (MOFECO-SS), which dynamically adjusts optimization strategies across different stages of the process, thereby enhancing overall efficiency. Extensive comparative analyses with existing algorithms demonstrate that MOFECO-SS consistently outperforms in solving the multi-objective optimization model, particularly in reducing total costs and carbon emissions while maintaining high levels of customer satisfaction. The symmetric nature of the distance matrix further aids in achieving balanced and optimized route planning. The results highlight that MOFECO-SS offers decision-makers flexible route planning options that balance cost efficiency with environmental sustainability, ultimately improving the effectiveness of cold chain logistics operations.

]]>Symmetry doi: 10.3390/sym16101304

Authors: Inés Cruz-Medel Daiana Priscila Rodrigues-de-Souza Francisco Alburquerque-Sendín

The human pelvis is a complex structure, which participates in the biomechanical functioning of the musculoskeletal system. Although it is considered a symmetrical entity, the morphology of the pelvis is subject to different factors that alter its anatomy, function or biomechanics, such as age, bipedal locomotion, obstetric changes and sexual dimorphism. However, how these factors influence pelvic asymmetry is unknown. Some evidence suggests that this condition leads to different pathological states, such as chronic low back pain, scoliosis, post-traumatic pelvic dysfunctions and obstetric changes. Therefore, pelvic asymmetries present a significant challenge in clinical practice due to their multifactorial nature and their potential impact on quality of life. Multidisciplinary research and collaboration are essential to improve understanding and develop more effective and specific identification and treatment approaches in the presence of pelvic asymmetries.

]]>Symmetry doi: 10.3390/sym16101302

Authors: Chao Zhang Guo-Zhi Li Maihemuti Wusiman Ge Yan Chang-Lin Yan Hua-Ping Wang

Pipes are the main structures serving as the lifeline for oil and gas transportation. However, they are prone to cracks, holes and other damages due to harsh working environments, which can lead to leakage incidents and result in significant economic losses. Therefore, the development of structural health monitoring systems with advanced online diagnostic methods is of great importance for identifying local damages and assessing the safety state of pipe structures. These efforts can guide rapid repairs and ensure the continuous, efficient and cost-effective transportation of oil and gas resources. To address this problem, this paper proposes the development of a pipe monitoring system based on quasi-distributed fiber Bragg grating (FBG) sensing technology. The SSI-COV method is employed to process the sensor responses and extract the modal parameters of the structure. Based on this foundation, an enhanced damage identification index is proposed, which mitigates the effects of support and excitation positions on damage identification. The pipe structure can be regarded as a continuous super-statical beam, and based on its structural symmetry, a unit structure, specifically a stainless-steel pipe with fixed ends, is regarded as the experimental subject. Impact experiments have been conducted to analyze its behavior in both undamaged and damaged states. The research indicates that by using the proposed modal parameter identification method and the ASMDI damage index, ASMDI exhibits peak values at damage locations of the pipe structure. This allows for the identification of structural damage with high accuracy, fast processing efficiency and strong robustness. The study provides an effective and reliable damage diagnosis method, which can contribute to the refinement and visualization of pipe structural health monitoring systems.

]]>Symmetry doi: 10.3390/sym16101303

Authors: Sushil Kumar Daniel Breaz Luminita-Ioana Cotîrlă Asena Çetinkaya

In this paper, we consider a subclass of normalized analytic functions associated with the hyperbolic secant function. We compute the sharp bounds on third- and fourth-order Hermitian&ndash;Toeplitz determinants for functions in this class. Moreover, we determine the bounds on second- and third-order Hankel determinants, as well as on the generalized Zalcman conjecture. We examine a Briot&ndash;Bouquet-type differential subordination involving the Bernardi integral operator. Finally, we obtain a univalent solution to the Briot&ndash;Bouquet differential equation, and discuss the majorization property for such function classes.

]]>Symmetry doi: 10.3390/sym16101301

Authors: Brian C. Peterson Patrick D. Farrell Casey W. Schoenebeck

Antlers are genetically coded to have bilateral symmetry. However, environmental stressors cause asymmetries between antlers. Previous studies have investigated fluctuating asymmetries on harvested white-tailed deer (Odocoileus virginianus Zimmermann, 1780). Cast antlers provide underutilized metrics that are not available prior to shedding. The objectives of this study were to quantify relative fluctuating asymmetry (RFA) between age groups and identify the best age-specific pre- and post-cast antler metrics to confirm an antler pair. We hypothesized lower RFA values for post-cast measurements than pre-cast measurements due to a lessened chance for damage when atop the head. Additionally, younger individuals were hypothesized to have higher RFA values due to greater susceptibility to environmental stressors. Cast antler pairs from 196 white-tailed deer were collected in Nebraska. We measured 14 available antler metrics per cast antler side classified by age group. The most symmetric measurements between antler sides included pedicle seal area, main beam length, and circumference. Antlers of older deer were consistently more symmetric than younger deer. When combining the top metrics and testing against random antler pairs, we found an 81.9&ndash;92.3% match rate for 1.5 and &ge;2.5-year-olds, respectively. Our findings provided a quantifiable method to assign antler pair classifications more confidently while documenting decreased symmetry in younger individuals.

]]>Symmetry doi: 10.3390/sym16101300

Authors: Edoardo Ballico

For all integers n&ge;1 and k&ge;2, the Hadamard product v1&#9733;&#8943;&#9733;vk of k elements of Kn+1 (with K being the complex numbers or real numbers) is the element v&isin;Kn+1 which is the coordinate-wise product of v1,&hellip;,vk (introduced by Cueto, Morton, and Sturmfels for a model in Algebraic Statistics). This product induces a rational map h:Pn(K)k&#10511;Pn(K). When K=C, k=2 and Xi(C)&sub;Pn(C), i=1,2 are irreducible, we prove four theorems for the case dimX2(C)=1, three of them with X2(C) as a line. We discuss the existence (non-existence) of a cancellation law for &#9733;-products and use the symmetry group of the Hadamard product. In the second part, we work over R. Under mild assumptions, we prove that by knowing X1(R)&#9733;&#8943;&#9733;Xk(R), we know X1(C)&#9733;&#8943;&#9733;Xk(C). The opposite, i.e., taking and multiplying a set of complex entries that are invariant for the complex conjugation and then seeing what appears in the screen Pn(R), very often provides real ghosts, i.e., images that do not come from a point of X1(R)&times;&#8943;&times;Xk(R). We discuss a case in which we certify the existence of real ghosts as well as a few cases in which we certify the non-existence of these ghosts, and ask several open questions. We also provide a scenario in which ghosts are not a problem, where the Hadamard data are used to test whether the images cover the full screen.

]]>Symmetry doi: 10.3390/sym16101299

Authors: Harshna Balhara Jainendra Kumar Singh Shaily Emmanuel N. Saridakis

We perform observational confrontation and cosmographic analysis of f(T,TG) gravity and cosmology. This higher-order torsional gravity is based on both the torsion scalar, as well as on the teleparallel equivalent of the Gauss&ndash;Bonnet combination, and gives rise to an effective dark-energy sector which depends on the extra torsion contributions. We employ observational data from the Hubble function and supernova Type Ia Pantheon datasets, applying a Markov chain Monte Carlo sampling technique, and we provide the iso-likelihood contours, as well as the best-fit values for the parameters of the power-law model, an ansatz which is expected to be a good approximation of most realistic deviations from general relativity. Additionally, we reconstruct the effective dark-energy equation-of-state parameter, which exhibits a quintessence-like behavior, while in the future the Universe enters into the phantom regime, before it tends asymptotically to the cosmological constant value. Furthermore, we perform a detailed cosmographic analysis, examining the deceleration, jerk, snap, and lerk parameters, showing that the transition to acceleration occurs in the redshift range 0.52&le;ztr&le;0.89, as well as the preference of the scenario for quintessence-like behavior. Finally, we apply the Om diagnostic analysis to cross-verify the behavior of the obtained model.

]]>Symmetry doi: 10.3390/sym16101298

Authors: Soon-Mo Jung Yang-Hi Lee Jaiok Roh

In this paper, we present a uniqueness theorem obtained by using direct calculation. This theorem is applicable to stability problems of functional equations whose solutions are monomial or generalized polynomial mappings of degree n. The advantage of this uniqueness theorem is that it simplifies the proof by eliminating the need to repeatedly and cumbersomely prove uniqueness in stability studies.

]]>Symmetry doi: 10.3390/sym16101296

Authors: Sérgio D. Correia Pedro M. Roque João P. Matos-Carvalho

In this paper, the concept of symmetry is used to design the efficient inference of a fall-detection algorithm for elderly people on embedded processors&mdash;that is, there is a symmetric relation between the model&rsquo;s structure and the memory footprint on the embedded processor. Artificial intelligence (AI) and, more particularly, Long Short-Term Memory (LSTM) neural networks are commonly used in the detection of falls in the elderly population based on acceleration measures. Nevertheless, embedded systems that may be utilized on wearable or wireless sensor networks have a hurdle due to the customarily massive dimensions of those networks. Because of this, the algorithms&rsquo; most popular implementation relies on edge or cloud computing, which raises privacy concerns and presents challenges since a lot of data need to be sent via a communication channel. The current work proposes a memory occupancy model for LSTM-type networks to pave the way to more efficient embedded implementations. Also, it offers a sensitivity analysis of the network hyper-parameters through a grid search procedure to refine the LSTM topology network under scrutiny. Lastly, it proposes a new methodology that acts over the quantization granularity for the embedded AI implementation on wearable devices. The extensive simulation results demonstrate the effectiveness and feasibility of the proposed methodology. For the embedded implementation of the LSTM for the fall-detection problem on a wearable platform, one can see that an STM8L low-power processor could support a 40-hidden-cell LSTM network with an accuracy of 96.52%.

]]>Symmetry doi: 10.3390/sym16101297

Authors: Maria de Fátima Brilhante Dinis Pestana Maria Luísa Rocha

Inferences on the location parameter &lambda; in location-scale families can be carried out using Studentized statistics, i.e., considering estimators &lambda;&tilde; of &lambda; and &delta;&tilde; of the nuisance scale parameter &delta;, in a statistic T=g(&lambda;&tilde;,&delta;&tilde;) with a sampling distribution that does not depend on (&lambda;,&delta;). If both estimators are independent, then T is an externally Studentized statistic; otherwise, it is an internally Studentized statistic. For the Gaussian and for the exponential location-scale families, there are externally Studentized statistics with sampling distributions that are easy to obtain: in the Gaussian case, Student&rsquo;s classic t statistic, since the sample mean &lambda;&tilde;=X&macr; and the sample standard deviation &delta;&tilde;=S are independent; in the exponential case, the sample minimum &lambda;&tilde;=X1:n and the sample range &delta;&tilde;=Xn:n&minus;X1:n, where the latter is a dispersion estimator, which are independent due to the independence of spacings. However, obtaining the exact distribution of Student&rsquo;s statistic in non-Gaussian populations is hard, but the consequences of assuming symmetry for the parent distribution to obtain approximations allow us to determine if Student&rsquo;s statistic is conservative or liberal. Moreover, examples of external and internal Studentizations in the asymmetric exponential population are given, and an ANalysis Of Spacings (ANOSp) similar to an ANOVA in Gaussian populations is also presented.

]]>Symmetry doi: 10.3390/sym16101295

Authors: Selcuk Yilmaz Murat Dener

Smart Grids are an area where next-generation technologies, applications, architectures, and approaches are utilized. These grids involve equipping and managing electrical systems with information and communication technologies. Equipping and managing electrical systems with information and communication technologies, developing data-driven solutions, and integrating them with Internet of Things (IoT) applications are among the significant applications of Smart Grids. As dynamic systems, Smart Grids embody symmetrical principles in their utilization of next-generation technologies and approaches. The symmetrical integration of Wireless Sensor Networks (WSNs) and energy harvesting techniques not only enhances the resilience and reliability of Smart Grids but also ensures a balanced and harmonized energy management system. WSNs carry the potential to enhance various aspects of Smart Grids by offering energy efficiency, reliability, and cost-effective solutions. These networks find applications in various domains including power generation, distribution, monitoring, control management, measurement, demand response, pricing, fault detection, and power automation. Smart Grids hold a position among critical infrastructures, and without ensuring their cybersecurity, they can result in national security vulnerabilities, disruption of public order, loss of life, or significant economic damage. Therefore, developing security approaches against cyberattacks in Smart Grids is of paramount importance. This study examines the literature on &ldquo;Cybersecurity with WSN in Smart Grids,&rdquo; presenting a systematic review of applications, challenges, and standards. Our goal is to demonstrate how we can enhance cybersecurity in Smart Grids with research collected from various sources. In line with this goal, recommendations for future research in this field are provided, taking into account symmetrical principles.

]]>Symmetry doi: 10.3390/sym16101294

Authors: Shrideh Al-Omari Wael Salameh Sharifah Alhazmi

This paper discusses definitions and properties of q-analogues of the gamma integral operator and its extension to classes of generalized distributions. It introduces q-convolution products, symmetric q-delta sequences and q-quotients of sequences, and establishes certain convolution theorems. The convolution theorems are utilized to accomplish q-equivalence classes of generalized distributions called q-Boehmians. Consequently, the q-gamma operators are therefore extended to the generalized spaces and performed to coincide with the classical integral operator. Further, the generalized q-gamma integral is shown to be linear, sequentially continuous and continuous with respect to some involved convergence equipped with the generalized spaces.

]]>Symmetry doi: 10.3390/sym16101293

Authors: Mohammed Alqahtani R. Keerthana S. Venkatesh M. Kaviyarasu

This work introduces the notion of a hesitant bipolar-valued intuitionistic fuzzy graph (HBVIFG), which reflects four different characterizations: membership with positive/negative aspects and non-membership with positive/negative aspects, incorporating multi-dimensional alternatives in all of its information. HBVIFG generalizes both HBVFG and BVHFG due to its diversified nature in observing four perspectives along with multiple attributes in a piece of information. Numerous studies, examples, and graphical representations emphasize the concept&rsquo;s distinctiveness and importance. The following graph theory terms are defined: strong directed HBVIFG, full directed HBVIFG, directed spanning HBVIFSG, directed HBVIFSG, and partial directed hesitant bipolar-valued intuitionistic fuzzy subgraph (HBVIFSG). Examples of operations utilizing two HBVIFGs are Cartesian, direct, lexicographical, and strong products. A scenario is used to generate the mapping of relations, which includes homomorphism, isomorphism, weak isomorphism, and co-weak isomorphism. We describe a directed HBVIFG application that employs an algorithm to determine the most dominant person and self-persistent person in a social system and a comparative study is also provided. The proposed method provides a more detailed framework for assessing the most dominant and self-persistent individual in a social network across multi-level attributes along with positive and negative side membership and non-membership grades in each element of a network.

]]>Symmetry doi: 10.3390/sym16101292

Authors: Zhengliang Chen

Based on the approximation spaces, the interval-valued intuitionistic fuzzy rough set (IVIFRS) plays an essential role in coping with the uncertainty and ambiguity of the information obtained whenever human opinion is modeled. Moreover, a family of flexible t-norm (TNrM) and t-conorm (TCNrM) known as the Aczel&ndash;Alsina t-norm (AATNrM) and t-conorm (AATCNrM) plays a significant role in handling information, especially from the unit interval. This article introduces a novel clustering model based on IFRS using the AATNrM and AATCNrM. The developed clustering model is based on the aggregation operators (AOs) defined for the IFRS using AATNrM and AATCNrM. The developed model improves the level of accuracy by addressing the uncertain and ambiguous information. Furthermore, the developed model is applied to the segmentation problem, considering the information about the income and spending scores of the customers. Using the developed AOs, suitable customers are targeted for marketing based on the provided information. Consequently, the proposed model is the most appropriate technique for the segmentation problems. Furthermore, the results obtained at different values of the involved parameters are studied.

]]>Symmetry doi: 10.3390/sym16101291

Authors: Simone Farinelli

The Dirac-Dolbeault operator for a compact K&auml;hler manifold is a special case of Dirac operator. The Green function for the Dirac Laplacian over a Riemannian manifold with boundary allows the expression of the values of the sections of the Dirac bundle in terms of the values on the boundary, extending the mean value theorem of harmonic analysis. Utilizing this representation and the Nash&ndash;Moser generalized inverse function theorem, we prove the existence of complex submanifolds of a complex projective manifold satisfying globally a certain partial differential equation under a certain injectivity assumption. Thereby, internal symmetries of Dolbeault and rational Hodge cohomologies play a crucial role. Next, we show the existence of complex submanifolds whose fundamental classes span the rational Hodge classes, proving the Hodge conjecture for complex projective manifolds.

]]>Symmetry doi: 10.3390/sym16101290

Authors: Fan Zhang Zhongsheng Chen

This paper introduces a novel Particle Swarm Optimization (RLPSO) algorithm based on reinforcement learning, embodying a fundamental symmetry between global and local search processes. This symmetry aims at addressing the trade-off issue between convergence speed and diversity in traditional algorithms. Traditional Particle Swarm Optimization (PSO) algorithms often struggle to maintain good convergence speed and particle diversity when solving multi-modal function problems. To tackle this challenge, we propose a new algorithm that incorporates the principles of reinforcement learning, enabling particles to intelligently learn and adjust their behavior for better convergence speed and richer exploration of the search space. This algorithm guides particle learning behavior through online updating of a Q-table, allowing particles to selectively learn effective information from other particles and dynamically adjust their strategies during the learning process, thus finding a better balance between convergence speed and diversity. The results demonstrate the superior performance of this algorithm on 16 benchmark functions of the CEC2005 test suite compared to three other algorithms. The RLPSO algorithm can find all global optimum solutions within a certain error range on all 16 benchmark functions, exhibiting outstanding performance and better robustness. Additionally, the algorithm&rsquo;s performance was tested on 13 benchmark functions from CEC2017, where it outperformed six other algorithms by achieving the minimum value on 11 benchmark functions. Overall, the RLPSO algorithm shows significant improvements and advantages over traditional PSO algorithms in aspects such as local search strategy, parameter adaptive adjustment, convergence speed, and multi-modal problem handling, resulting in better performance and robustness in solving optimization problems. This study provides new insights and methods for the further development of Particle Swarm Optimization algorithms.

]]>Symmetry doi: 10.3390/sym16101289

Authors: Xinghang Xu Du Cheng Dan Wang Qingliang Li Fanhua Yu

Pareto dominance-based algorithms face a significant challenge in handling many-objective optimization problems. As the number of objectives increases, the sharp rise in non-dominated individuals makes it challenging for the algorithm to differentiate their quality, resulting in a loss of selection pressure. The application of the penalty-based boundary intersection (PBI) method can balance convergence and diversity in algorithms. The PBI method guides the evolution of individuals by integrating the parallel and perpendicular distances between individuals and reference vectors, where the penalty factor is crucial for balancing these two distances and significantly affects algorithm performance. Therefore, a comprehensive adaptive penalty scheme was proposed and applied to NSGA-III, named caps-NSGA-III, to achieve balance and symmetry between convergence and diversity. Initially, each reference vector&rsquo;s penalty factor is computed based on its own characteristic. Then, during the iteration process, the penalty factor is adaptively adjusted according to the evolutionary state of the individuals associated with the corresponding reference vector. Finally, a monitoring strategy is designed to oversee the penalty factor, ensuring that adaptive adjustments align with the algorithm&rsquo;s needs at different stages. Through a comparison involving benchmark experiments and two real-world problems, the competitiveness of caps-NSGA-III was demonstrated.

]]>Symmetry doi: 10.3390/sym16101288

Authors: Serkan Onar

This research aims to introduce and explore the theory of neutrosophic soft hyperalgebras (NSHAs), focusing on their core principles and potential applications in decision-making under uncertainty. By defining key operations such as intersection and union, we clarify the foundational characteristics of NSHAs and their relationship to soft hyperalgebras. The concepts of &xi;&beta;-identity NSHA and &xi;-absolute NSHA are also examined to better understand their properties. The practical relevance of NSHA is demonstrated through applications in various fields, highlighting its adaptability in addressing complex decision-making scenarios. This approach offers a novel, more precise method for navigating uncertainty in areas such as project methodology selection, sensitivity analysis, and AI chatbot selection.

]]>Symmetry doi: 10.3390/sym16101287

Authors: Konglin Zhu Fengjuan Wu Fei Wang Tingda Shen Hao Wu Bowei Xue Yu Liu

The circulation of digital assets has become increasingly crucial in today&rsquo;s digital economy, reflecting both its growing importance and the challenges it faces. Blockchain technology, with its inherent symmetry, has emerged as a transformative force in facilitating digital asset circulation, addressing various issues related to security, efficiency, and transparency. This paper aims to advance the development of digital asset circulation technologies by focusing on four key blockchain-based technologies: smart contracts, consensus algorithms, cross-chain technology, and decentralized exchanges. These technologies embody symmetry in their structure and operation, ensuring balanced and secure asset management across decentralized networks. This paper reviews the evolution of these key technologies, highlighting their contributions to the digital asset ecosystem. It explores effective application cases and analyzes the current challenges each technology faces. Additionally, this paper provides insights into potential future developments and directions to address these challenges and enhance the overall efficiency and reliability of digital asset circulation.

]]>Symmetry doi: 10.3390/sym16101286

Authors: Marcin Michalak

A bicluster consists of a subset of rows and columns of a given matrix, whose intersection defines the region (bicluster) of values of precisely defined condition. Through the decades, a variety of biclustering techniques have been successfully developed. Recently, it was proved that many possible patterns defined in two-dimensional data could be found with the application of Boolean reasoning. The provided theorems showed that any existing pattern in the data could be unequivocally encoded as an implicant of a proper Boolean function. Moreover, a prime implicant of that function encoded the inclusion-maximal (non-extendable) pattern. On the other hand, the definition of some two-dimensional patterns may be easily extended to three-dimensional patterns (triclusters) as well as to any number of dimensions (n-clusters). This paper presents a new approach for searching for three- and higher-dimensional simple patterns in continuous data with Boolean reasoning. Providing the definition of the Boolean function for this tasks, it is shown that the similar correspondence&mdash;implicants encode patterns, and prime implicants encode inclusion-maximal patterns&mdash;has a strong mathematical background: the proofs of appropriate theorems are also presented in this paper.

]]>Symmetry doi: 10.3390/sym16101285

Authors: Guojiang Wu Yong Guo Yanlin Yu

This article introduces two kinds of processing techniques to solve Jacobian elliptic equations and obtain rich periodic wave solutions. Then, the equation was used as an auxiliary equation to solve the (3+1)-dimensional modified Korteweg de Vries&ndash;Zakharov&ndash;Kuznetsov (mKDV-ZK) equation. Combined with the mapping method, a large number of new types of exact periodic wave solutions were obtained, many of which were rarely found in previous research. Numerical simulations have demonstrated the evolution of various periodic waves in (3+1)-dimensional mKDV-ZK. The solutions and wave phenomena obtained in this article will help expand our understanding of the equation.

]]>Symmetry doi: 10.3390/sym16101284

Authors: Mdi Begum Jeelani Nadiyah Hussain Alharthi

In the last few years, the conjunctivitis adenovirus disease has been investigated by using the concept of mathematical models. Hence, researchers have presented some mathematical models of the mentioned disease by using classical and fractional order derivatives. A complementary method involves analyzing the system of fractal fractional order equations by considering the set of symmetries of its solutions. By characterizing structures that relate to the fundamental dynamics of biological systems, symmetries offer a potent notion for the creation of mechanistic models. This study investigates a novel mathematical model for conjunctivitis adenovirus disease. Conjunctivitis is an infection in the eye that is caused by adenovirus, also known as pink eye disease. Adenovirus is a common virus that affects the eye&rsquo;s mucosa. Infectious conjunctivitis is most common eye disease on the planet, impacting individuals across all age groups and demographics. We have formulated a model to investigate the transmission of the aforesaid disease and the impact of vaccination on its dynamics. Also, using mathematical analysis, the percentage of a population which needs vaccination to prevent the spreading of the mentioned disease can be investigated. Fractal fractional derivatives have been widely used in the last few years to study different infectious disease models. Hence, being inspired by the importance of fractal fractional theory to investigate the mentioned human eye-related disease, we derived some adequate results for the above model, including equilibrium points, reproductive number, and sensitivity analysis. Furthermore, by utilizing fixed point theory and numerical techniques, adequate requirements were established for the existence theory, Ulam&ndash;Hyers stability, and approximate solutions. We used nonlinear functional analysis and fixed point theory for the qualitative theory. We have graphically simulated the outcomes for several fractal fractional order levels using the numerical method.

]]>Symmetry doi: 10.3390/sym16101283

Authors: Yuxun Zhang Jiang Zhou

An infinite homogeneous tree is a special type of graph that has a completely symmetrical structure in all directions. For an infinite homogeneous tree T=(V,E) with the natural distance d defined on graphs and a weighted measure &mu; of exponential growth, the authors introduce the variable Lebesgue space Lp(&middot;)(&mu;) over (V,d,&mu;) and investigate it under the global H&ouml;lder continuity condition for p(&middot;). As an application, the strong and weak boundedness of the maximal operator relevant to admissible trapezoids on Lp(&middot;)(&mu;) is obtained, and an unbounded example is presented.

]]>Symmetry doi: 10.3390/sym16101282

Authors: Xiang Gong Ting Kou Yan Li

The communication of Industrial Internet of Things (IIoT) devices faces important security and privacy challenges. With the rapid increase in the number of devices, it is difficult for traditional security mechanisms to balance performance and security. Although schemes based on encryption and authentication exist, there are still difficulties in achieving lightweight security. In this paper, an authentication and key exchange scheme combining hardware security features and modern encryption technology is proposed for the MQTT-SN protocol, which is not considered security. The scheme uses Physical Unclonable Functions (PUFs) to generate unpredictable responses, and combines random numbers, time stamps, and shared keys to achieve two-way authentication and secure communication between devices and broker, effectively preventing network threats such as replay and man-in-the-middle attacks. Through verification, the proposed scheme has proved effective in terms of security and robustness, has computational and communication cost advantages compared with recent schemes, and provides higher availability.

]]>Symmetry doi: 10.3390/sym16101281

Authors: Qasim Ali Shakir Adel Salim Tayyah Daniel Breaz Luminita-Ioana Cotîrlă Eleonora Rapeanu Fethiye Müge Sakar

This paper investigates the third Hankel determinant, denoted H3(1), for functions within the subclass RS&sum;*(&lambda;) of bi-univalent functions associated with crescent-shaped regions &phi;&#10629;z=z+1+z2. The primary aim of this study is to establish upper bounds for H3(1). By analyzing functions within this specific geometric context, we derive precise constraints on the determinant, thereby enhancing our understanding of its behavior. Our results and examples provide valuable insights into the properties of bi-univalent functions in crescent-shaped domains and contribute to the broader theory of analytic functions.

]]>Symmetry doi: 10.3390/sym16101280

Authors: Danyan Xie Wenyi Yao Wenbo Sun Zhenyu Song

Strawberry crops are susceptible to a wide range of pests and diseases, some of which are insidious and diverse due to the shortness of strawberry plants, and they pose significant challenges to accurate detection. Although deep learning-based techniques to detect crop pests and diseases are effective in addressing these challenges, determining how to find the optimal balance between accuracy, speed, and computation remains a key issue for real-time detection. In this paper, we propose a series of improved algorithms based on the YOLOv8 model for strawberry disease detection. These include improvements to the Convolutional Block Attention Module (CBAM), Super-Lightweight Dynamic Upsampling Operator (DySample), and Omni-Dimensional Dynamic Convolution (ODConv). In experiments, the accuracy of these methods reached 97.519%, 98.028%, and 95.363%, respectively, and the F1 evaluation values reached 96.852%, 97.086%, and 95.181%, demonstrating significant improvement compared to the original YOLOv8 model. Among the three improvements, the improved model based on CBAM has the best performance in training stability and convergence, and the change in each index is relatively smooth. The model is accelerated by TensorRT, which achieves fast inference through highly optimized GPU computation, improving the real-time identification of strawberry diseases. The model has been deployed in the cloud, and the developed client can be accessed by calling the API. The feasibility and effectiveness of the system have been verified, providing an important reference for the intelligent research and application of strawberry disease identification.

]]>Symmetry doi: 10.3390/sym16101279

Authors: Zhimo Jian Chaoqian Luo Tianyi Zhou Gang Peng Yajun Yin

In recent years, our research on biomechanical and biophysical problems has involved a series of symmetry issues. We found that the fundamental laws of the aforementioned problems can all be characterized by fractal operators, and each type of operator possesses rich invariant properties. Based on the invariant properties of fractal operators, we discovered that the symmetry evolution laws of functional fractal trees in the physical fractal space can reveal the intrinsic correlations between special functions. This article explores the fractional-order correlation between special functions inspired by bone fractal operators. Specifically, the following contents are included: (1) showing the intrinsic expression in the convolutional kernel function of bone fractal operators and its correlation with special functions; (2) proving the following proposition: the convolutional kernel function of bone fractal operators is still related to the special functions under different input signals (external load, external stimulus); (3) using the bone fractal operators as the background and error function as the core, deriving the fractional-order correlation between different special functions.

]]>Symmetry doi: 10.3390/sym16101278

Authors: Aniruddha Agrawal Berker Bilgin Amrutha K. Haridas

The benefits of utilizing Switched Reluctance Motor (SRM) drives in traction applications can be realized fully by improving the electromagnetic performance of the machine in the generating mode of operation. This is because the generating capability of an SRM drive could be utilized for regenerative braking and also for the machine to generate power for the vehicle while the engine is in operation. In this paper, a current profiling-based control strategy is proposed to reduce the torque ripple in an SRM drive in the generating mode. The reference current profile is determined using a multi-step computation method to minimize torque ripple and maximize the average torque. The reference current profile is derived based on the reference torque command by utilizing the torque&ndash;current&ndash;angle look up table. The flux linkage characteristics of the SRM are considered when deriving the phase reference current profile. Then, the performance of the proposed profiling method, analytical linear and cubic torque sharing functions (TSFs), and the average torque optimization scheme are compared using simulation results. Finally, an experimental correlation is performed to validate the efficacy of the proposed control scheme.

]]>Symmetry doi: 10.3390/sym16101277

Authors: Zhenwei Zhang Yutong Luo Guisheng Yang Shaozheng Zhang Zhengwei Wang

During the transient process of load rejection, the hydraulic pressure applied to the pump-turbine and plant concrete changes dramatically and induces high dynamic stress on the spiral case. The preloading spiral case has been widely used in large-scale pumped-storage power stations due to its excellent load-bearing capacity. However, studies on the impact of preloading pressure on the structural response during load rejection are still few in number. In this paper, 3D flow domain and structural models of a prototype pump-turbine are designed to analyze the hydraulic characteristics and flow-induced dynamic behavior of the preloading steel spiral case under different preloading pressures during load rejection. The results show that the asymmetric design of the logarithmic spiral lines ensures an axially symmetric potential flow within the spiral case domain with uniform pressure distribution. Higher preloading pressure provides larger preloading clearance, leading to greater flow-induced deformation and stress, with their maximum values located at the mandoor and the inner edge, respectively. The combined effect of the asymmetrical shape, internal hydraulic pressure and unbalanced hydraulic force leads to an asymmetrical preloading clearance distribution, resulting in an asymmetrical distribution along the axial direction but a symmetrical characteristic near the waistline of the structural response. Stress variations at sections and between sections share similar characteristics during load rejection. It follows the same trend as the hydraulic pressure under lower preloading pressures, while there is a delayed peak of stress due to the delayed contact phenomenon when the preloading pressure reaches the maximum static head. The conclusions provide scientific guidance for optimizing the preloading pressure selection and structural design for the stable operation of units.

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